If rArr int(-1)^(-4) f(x)dx= 4 and int(2...

If `rArr int_(-1)^(-4) f(x)dx= 4 and int_(2)^(-4) (3-f(x))dx=7` , then the volue of `rArr int_(-2)^(1) f(-x)dx` is

A

2

B

`-3`

C

5

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

D

We have,
` underset(2)overset(-4)int (3-f(-x))dx-7`
`rArr underset(2)overset(-4)int 3 dx-underset(2)overset(-4)int f(x) dx=7`
`rArr 3(-4-2)-underset(2)overset(-4)intf(x)dx=7`
`rArr underset(2)overset(-4)intf(x)dx=-25`
`rArr underset(-4)overset(2)intf(x)dx=25`
`rArr underset(-4)overset(-1)intf(x)dx+underset(-1)overset(2)int f(x)dx=25`
`rArr -4+underset(-1)overset(2)intf(x)dx=25" " [ :. underset(-1)overset(0-4)intf(x)dx=4]`
`rArr underset(-1)overset(2)intf(x)dx=29`
`rArr underset(-1)overset(2)intf(-t)dt=29,"where" t=-x`
`rArr underset(-2)overset(1)intf(-t)dt=-29`

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