PROPERTIES OF DEFINITE AND INDEFINITE INTEGRALS

Property 1 :

Integration is independent of change of variables provided the limits of integration remain the same.

Property 2 :

If the limits of definite integral are interchanged, then the value of integral changes its sign only.

Property 3 :

Property 4 :

Property 5 :

If f(x) is integrable on a closed interval containing the three numbers a, b and c, then regardless of the order of a, b and c.

Property 6 :

Property 7 :

Property 8 :

To check if the function is odd or even, in the given function f(x) apply x  =  -x

• If f(-x)  =  f(x), then f(x) is even.
• If f(-x)  =  -f(x), then f(x) is odd.

Properties of Indefinite Integrals

Evaluate the following problems using properties of integration.

Question 1 :

The given function is odd.

Question 2 :

The given function is odd.

Question 3 :

Question 4 :

The function f(x) is even.

Question 5 :

The function f(x) is even.

=  1 - (1/2) [-1/3+1]

=  1-(1/2)[2/3]

=  1-(1/3)

=  2/3

Question 6 :

The function f(x) is odd.

Question 7 :

2I  =  0

I  =  0

So, the answer is 0.

Question 8 :

Question 9 :

Question 10 :

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