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If (1 sin t)/(1 + t) dt = alpha, then th...

If `(1 sin t)/(1 + t) dt = alpha`, then that value of the integral :
`int_(4pi - 2)^(4pi) (sin t/2)/(4pi + 2 - t) dt` in terms of `alpha` is given by :

A

`2 alpha`

B

`-2 alpha`

C

`alpha`

D

`-alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
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MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
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  2. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  3. If (1 sin t)/(1 + t) dt = alpha, then that value of the integral : i...

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  4. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

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  5. Let f(x) = int1^x sqrt(2 - t^2)dt. Then the real roots of the equation...

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  8. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

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  9. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

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  10. If f(x) = int(x^2)^(x^2 + 1) e^(-t^2) dt, find the interval in which f...

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  11. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

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  12. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

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  13. If I(1) = int0^(1) 2^(x^(2)) dx, I(2) = int0^(1) 2^(x^(3)) dx, I(3) = ...

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  14. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

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  16. Let F(x) = f(x) + f(1/x), where , f(x) = int1^x (log t)/(1 + t) dt. Th...

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  17. The solution for x of the equation : int(sqrt2)^(x) (dt)/(tsqrt(t^2 - ...

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  18. Let I = int0^1 (sin x)/(sqrtx) dx and J = int0^1 (cos x)/(sqrtx) dx. T...

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  19. If I(m,n) = int0^1 t^m (1 + t)^n dt , m, n in R, then I(m, n) is :

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  20. If f(x) is differentiable and int0^(t^2) x f(x) dx = 2/5 t^5, then f (...

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