## There are many practical applications of Definite Integration.

## Definite integrals can be used to determine the mass of an object if its density function is known. We can also find work by integrating a force function, and the force exerted on an object submerged in a liquid. The most important application of Definite Integration is finding the area under the curve.

## Let f be a continuous function defined on the closed interval [a, b] and F be an antiderivative of f then

##
∫
^{
b
}
_{
a
}
f(x) dx = [F (x)]
^{
b
}
_{
a
}
= F(b) - F(a)

## It is very useful because it gives us a method of calculating the definite integral more easily. There is no need to keep integration constant C because if we consider F(x)+C instead of F(x).

##
**
Question 1
**

##
∫
^{
3
}
_{
2
}
x
^{
2
}
dx is equal to:

## (a) 7/3

## (b) 9

## c) 19/3

## (d) 1/3

This question is inspired from Question 30 - CBSE Class 12 - Sample Paper for 2020 Boards

##
**
Question 2
**

##
∫
^{
√3
}
_{
1
}
dx/1 + x
^{
2
}
is equal to:

## (a) π/3

## (b) 2π/3

## (c) π/6

## (d) π/12

##
**
Question 3
**

##
∫
^{
1
}
_{
-1
}
(x + 1) dx is equal to:

## (a) −1

## (b) 2

## (c) 1

## (d) 3

##
**
Question 4
**

##
∫
^{
3
}
_{
2
}
1/x dx is equal to:

## (a) 3/2

## (b) 1/2

## (c) log(3/2)

## (d) log(2)

##
**
Question 5
**

##
∫
^{
5
}
_{
4
}
e
^{
x
}
dx is equal to:

## (a) 1

##
(b) e
^{
5
}
- 1

## (c) e

##
(d) e
^{
5
}
- e
^{
4
}