The document discusses integrals and their use in calculating areas and volumes. It defines an integral as combining infinitesimal data to determine displacement, area, volume, and other concepts. The document provides an example of calculating the indefinite integral of the function f(x)=x as 1/2x^2 + C and the definite integral from 0 to 3 of f(x)=x as 4.5 by using the integral formula and verification with the area of a rectangle formula.

2. Md Habibur Rahman
152-15-6040

3. Integral
displacement, area, volume, and other concepts that arise by
combining infinitesimal data.

4. Integral
⎰f (x) = ⎰ (x) dx
=½ 𝑥2
+ C
Let , Y
X
1 3 5
1
3
5
f (x) = x
indefinite integral

5. Integral
Let , Y
X
1 3 5
1
3
5
f (x) = x
0
= 0
3
𝑥 𝑑𝑥
=[½ 𝑥2
]0
3
=1/2 (9-0)
=4.5
1
2
∗ 𝐵𝑎𝑠𝑒 ∗ 𝐻𝑖𝑔ℎ𝑡
=0.5 *3 *3
=4.5
finite integral

6. Integral
Y
X
1 3 5
1
3
5
0

7. 3𝑑𝑥 = 3𝑥
3𝑥 𝑑𝑥 𝑑𝑥 = 3/2𝑥2
3/2𝑥2
𝑑𝑥 𝑑𝑥 𝑑𝑥 = 2𝑥3
x
y
y
x
y
x
f(x)=3
If the equation is,
f(x) = 3
f(x)=3x
𝑓 𝑥 = 3/2𝑥2
Integral