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Evaluate the following : int(4)^(7)((...

Evaluate the following :
`int_(4)^(7)((11-x)^(3))/(x^(3)+(11-x)^(3))dx`

A

1

B

`1//2`

C

`3//2`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I = int_(4)^(7) ((11- x)^(2))/(x^2 + (11 - x)^(2)) dx " " … (i)`
`= int_(4)^(7) (x^(2))/((11 - x)^(2) + x^(2)) dx " " … (ii)`
On adding Eqs. (i) and (ii) , we get
`2 I = int _(4)^(7) 1 dx = [x]_(4)^(7) = 3`
`implies I = (3)/(2)`
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