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Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3...

Evaluate: `int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7,` then find the value of `int_-1^(2)f(x)dxdot`

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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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
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  3. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

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  11. For any n in N, int(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to

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  12. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  13. If I(n)=int(0)^(pi//4) tan^(n)x dx, then (1)/(I(2)+I(4)),(1)/(I(3)+I...

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  14. Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x...

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  19. The value of the integral int(0)^(pi//2) sin 2n x cot x dx, where n ...

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