SlideShare a Scribd company logo
1 of 5
Integrals 
JENNIFER DEAN
What is an integral? 
 An integral is the reverse operation of a derivative. While the 
derivative will give the slope of a tangent line, an integral will give 
the area under a curve.
How do we integrate functions? 
 To integrate the aforementioned function, one would have to do 
the reverse of a derivative. 
 f'(x)= x^2 
 f(x)= (1/2+1)x^(2+1) +C=(.3333)x^3 +C 
 Add one to the exponent, and divide the unit by that number and 
add the constant by inserting a +C at the end.
Example Problem 
 F'(x) = 3x^2 + 2x +1 
 F(x)=? 
 G'(x)= 12x^2+12x+12 
 G(x)=?
Example Answers 
 F'(x) = 3x^2 + 2x +1 
 F(x)=x^3 + x^2 +x +C 
 G'(x)= 12x^2+12x+12 
 G(x)=4x^3 + 6x^2 + 12x +C

More Related Content

What's hot

Parts of quadratic function and transforming to general form to vertex form a...
Parts of quadratic function and transforming to general form to vertex form a...Parts of quadratic function and transforming to general form to vertex form a...
Parts of quadratic function and transforming to general form to vertex form a...
rowenaCARINO
 
Piecewise Functions
Piecewise FunctionsPiecewise Functions
Piecewise Functions
swartzje
 
Area Under the Curve
Area Under the CurveArea Under the Curve
Area Under the Curve
alexbeja
 

What's hot (20)

Integration
IntegrationIntegration
Integration
 
Theorem 4 of basic fundamental of integral
Theorem 4 of basic fundamental of integral Theorem 4 of basic fundamental of integral
Theorem 4 of basic fundamental of integral
 
3.4 Polynomial Functions and Their Graphs
3.4 Polynomial Functions and Their Graphs3.4 Polynomial Functions and Their Graphs
3.4 Polynomial Functions and Their Graphs
 
Parts of quadratic function and transforming to general form to vertex form a...
Parts of quadratic function and transforming to general form to vertex form a...Parts of quadratic function and transforming to general form to vertex form a...
Parts of quadratic function and transforming to general form to vertex form a...
 
L6 continuity
L6 continuityL6 continuity
L6 continuity
 
Application of derivatives 2 maxima and minima
Application of derivatives 2  maxima and minimaApplication of derivatives 2  maxima and minima
Application of derivatives 2 maxima and minima
 
Standard form solve equations
Standard form solve equationsStandard form solve equations
Standard form solve equations
 
Polynomials and Curve Fitting in MATLAB
Polynomials and Curve Fitting in MATLABPolynomials and Curve Fitting in MATLAB
Polynomials and Curve Fitting in MATLAB
 
Different types of functions
Different types of functionsDifferent types of functions
Different types of functions
 
Piecewise Functions
Piecewise FunctionsPiecewise Functions
Piecewise Functions
 
Scientific Computing II Numerical Tools & Algorithms - CEI40 - AGA
Scientific Computing II Numerical Tools & Algorithms - CEI40 - AGAScientific Computing II Numerical Tools & Algorithms - CEI40 - AGA
Scientific Computing II Numerical Tools & Algorithms - CEI40 - AGA
 
Area Under the Curve
Area Under the CurveArea Under the Curve
Area Under the Curve
 
Graph of a linear function
Graph of a linear functionGraph of a linear function
Graph of a linear function
 
Business Math Chapter 2
Business Math Chapter 2Business Math Chapter 2
Business Math Chapter 2
 
Graph of quadratic function
Graph of quadratic functionGraph of quadratic function
Graph of quadratic function
 
Graphing polynomials
Graphing polynomialsGraphing polynomials
Graphing polynomials
 
1 13s-f
1 13s-f1 13s-f
1 13s-f
 
Class 2 Math I
Class 2 Math IClass 2 Math I
Class 2 Math I
 
Modul 3 quadratic function
Modul 3 quadratic functionModul 3 quadratic function
Modul 3 quadratic function
 
Modeling with quadratic functions
Modeling with quadratic functionsModeling with quadratic functions
Modeling with quadratic functions
 

Viewers also liked

Sesion 5
Sesion 5Sesion 5
Sesion 5
al_mita
 
Projet sur les carrières
Projet sur les carrièresProjet sur les carrières
Projet sur les carrières
ame0591
 
VISWAPAVAN _2015_v1
VISWAPAVAN _2015_v1VISWAPAVAN _2015_v1
VISWAPAVAN _2015_v1
viswa pavan
 
La princesita hechizada
La princesita hechizadaLa princesita hechizada
La princesita hechizada
DaNii RiiVe
 

Viewers also liked (18)

Sesion 5
Sesion 5Sesion 5
Sesion 5
 
Projet sur les carrières
Projet sur les carrièresProjet sur les carrières
Projet sur les carrières
 
Grooming
GroomingGrooming
Grooming
 
VISWAPAVAN _2015_v1
VISWAPAVAN _2015_v1VISWAPAVAN _2015_v1
VISWAPAVAN _2015_v1
 
Sesión 2
Sesión 2Sesión 2
Sesión 2
 
Final essay
Final essayFinal essay
Final essay
 
教材教法
教材教法教材教法
教材教法
 
Comandos d ecisco
Comandos d eciscoComandos d ecisco
Comandos d ecisco
 
Oficina de documentos - cras nordeste
Oficina de documentos - cras nordesteOficina de documentos - cras nordeste
Oficina de documentos - cras nordeste
 
Nefroesclerosis
NefroesclerosisNefroesclerosis
Nefroesclerosis
 
NEFROLOGIA CLINICA: Glomerulonefritis rapidamente progresiva
NEFROLOGIA CLINICA: Glomerulonefritis rapidamente progresivaNEFROLOGIA CLINICA: Glomerulonefritis rapidamente progresiva
NEFROLOGIA CLINICA: Glomerulonefritis rapidamente progresiva
 
Glomerulonefritis
GlomerulonefritisGlomerulonefritis
Glomerulonefritis
 
La princesita hechizada
La princesita hechizadaLa princesita hechizada
La princesita hechizada
 
Presentación curso web 2.0
Presentación curso web 2.0Presentación curso web 2.0
Presentación curso web 2.0
 
Inglés
InglésInglés
Inglés
 
Startups , PME Entreprises technologiques : 10 conseils pour performer dans s...
Startups , PME Entreprises technologiques : 10 conseils pour performer dans s...Startups , PME Entreprises technologiques : 10 conseils pour performer dans s...
Startups , PME Entreprises technologiques : 10 conseils pour performer dans s...
 
Aspectos importantes de una criptomoneda
Aspectos importantes de una criptomonedaAspectos importantes de una criptomoneda
Aspectos importantes de una criptomoneda
 
Mythes et legendes des TIC
Mythes et legendes des TICMythes et legendes des TIC
Mythes et legendes des TIC
 

Recently uploaded

Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
ZurliaSoop
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
negromaestrong
 
Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please Practise
AnaAcapella
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ciinovamais
 

Recently uploaded (20)

microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.ppt
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy Consulting
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
 
Micro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdfMicro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdf
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and Modifications
 
General Principles of Intellectual Property: Concepts of Intellectual Proper...
General Principles of Intellectual Property: Concepts of Intellectual  Proper...General Principles of Intellectual Property: Concepts of Intellectual  Proper...
General Principles of Intellectual Property: Concepts of Intellectual Proper...
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The Basics
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
 
Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please Practise
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
 
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
 
Sociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning ExhibitSociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning Exhibit
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 

Integrals

  • 2. What is an integral?  An integral is the reverse operation of a derivative. While the derivative will give the slope of a tangent line, an integral will give the area under a curve.
  • 3. How do we integrate functions?  To integrate the aforementioned function, one would have to do the reverse of a derivative.  f'(x)= x^2  f(x)= (1/2+1)x^(2+1) +C=(.3333)x^3 +C  Add one to the exponent, and divide the unit by that number and add the constant by inserting a +C at the end.
  • 4. Example Problem  F'(x) = 3x^2 + 2x +1  F(x)=?  G'(x)= 12x^2+12x+12  G(x)=?
  • 5. Example Answers  F'(x) = 3x^2 + 2x +1  F(x)=x^3 + x^2 +x +C  G'(x)= 12x^2+12x+12  G(x)=4x^3 + 6x^2 + 12x +C