In this section we shall see how the properties of definite integrals are useful to evaluate definite integrals
Example 1
Solution:
Example 2
Solution:
Example 3
Prove that
Solution:
Adding (i) and (ii)
Example 4
Prove thatÂ
Solution:
Put 2a-x so that -dx=dt or dx=-dt
Now, x=0, t= 2a-0 and x=a , t=2a-a=a
Example 5
Prove thatÂ
Solution:
Put 2a-t =x, so that dx=-dt. Also x=a, t=a and x=2a, t=0
Example 6
Solution:
So, f(x) is an even function.