## 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

##
Β β«
^{
b
}
_{
a
}
f(x)Β 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).Β

##
**
Question 1
**

##
β«
^{
3
}
_{
2
}
x
^{
2
}
Β dx is equal to:

## (a) 7/3

## (b) 9Β

## c) 19/3Β

## (d) 1/3

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

##
**
Question 2
**

##
β«
^{
β3
}
_{
1
}
dx/1 + x
^{
2
}
Β is equal to:

## (a) Ο/3 Β Β Β

## (b) 2Ο/3Β

## (c) Ο/6Β

## (d) Ο/12

##
**
Question 3
**

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

## (a) β1Β

## (b) 2Β

## (c) 1Β

## (d) 3

##
**
Question 4
**

##
β«
^{
3
}
_{
2Β
}
1/xΒ dx is equal to:

## (a) 3/2Β

## (b) 1/2Β

## (c) log(3/2)

## (d) log(2)

Β

##
**
Question 5
**

##
β«
^{
5
}
_{
4Β
}
e
^{
x
}
Β dx is equal to:

## (a) 1Β

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

## (c) eΒ

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

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