IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
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Calculus I - Functions, Integrals, and Derivatives
1. Applied Calculus I β MTH 271
Integrals of Functions (Anti-Derivatives)
Functions and their Inverses
Examples:
Function Inverse
π¦ = 3π₯ β 7
π¦ =
π₯ + 7
3
2. 1
3
7
-1
2
14
π¦ = 3π₯ β 7
X Y
- 1
2
14
1
3
7
π¦ =
π₯ + 7
3
X Y
Function:
Inverse Function (of π¦ = 3π₯ β 7
3. Applied Calculus I β MTH 271
Integrals of Functions (Anti-Derivatives)
Functions and their Inverses
Examples:
Function Inverse
π¦ = 3π₯ β 7
π¦ =
π₯ + 7
3
π¦ = π π₯
π¦ = ln π₯
π¦β²
π¦
ππ¦
ππ₯
4. π¦ = 5π₯4
Function Derivative
π¦β² = 20π₯3π¦ = 5π₯4 + 35
π¦ = 5π₯4 β 163
The Derivative Function
This function (the derivative function) is not one-to-one so its
inverse is not a function.
The inverse (the integral of π¦β² = 20π₯) can be expressed as:
π¦ = 5π₯4 + πΆ , C being any real number.
5. π(π₯) = 5π₯4
+ πΆ
π(π₯) = 20π₯3If
represents a mathematical model of some process,
then we need more information to identify its integral function.
Example, if we know that at x = 0, y = 25, then C = 25,
π π₯ = 5π₯4 + 25
then,