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f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx...

`f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt`
The value of `int_(0)^(pi//2) f(x)dx` is

A

`1`

B

`-2`

C

`-1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
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CENGAGE-DEFINITE INTEGRATION -Exercise (Comprehension)
  1. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  2. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  3. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  4. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  5. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  6. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  7. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

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  8. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt f(x) is not invertibl...

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  9. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The value of int(0)^(...

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  10. Let u=int0^oo (dx)/(x^4+7x^2+1 and v=int0^x (x^2dx)/(x^4+7x^2+1) then

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  11. Let u=int0^oo (dx)/(x^4+7x^2+1 and v=int0^x (x^2dx)/(x^4+7x^2+1) then

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  12. If f(x)=int(0)^(1)(dt)/(1+|x-t|),x epsilonR the value of f'(1//2) is...

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  13. If f(x)=int(0)^(1)(dt)/(1+|x-t|),x epsilonR Which of the following ...

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  14. Let f be a differentiable function satisfying int(0)^(f(x))f^(-1)(t)d...

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  15. Let f be a differentiable function satisfying int(0)^(f(x))f^(-1)(t)d...

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  16. If U(n)=int(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of...

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  17. If Un=int0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zer...

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  18. Data could not be retrieved.

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  19. Data could not be retrieved.

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  20. Let the definite integral be defined by the formula int(a)^(b)f(x)dx=(...

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