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For any integer n, the integral : int0^(...

For any integer n, the integral : `int_0^(pi) e^(cos^2) cos^(3) (2n + 1)x dx` has the value :

A

`pi`

B

`1`

C

`0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
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  2. Let f : R to R be a differentiable function and f(1) = 4, then the val...

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  3. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

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  4. If In = int0^(pi//4) tan^n theta d theta, then for any +ve integer n, ...

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  5. int0^1 |sin 2 pi x| dx is equal to :

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  6. If f(x) = f(a - x), then int0^(a) xf(x) dx is equal to :

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  7. Let f(x) = {:[(e^(cos x) sinx",", "for" |x| le 2),(2,"otherwise"):} th...

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  8. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

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  9. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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

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

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

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  14. Let T > 0 be a fixed real number. Suppose f is a continuous function s...

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  15. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

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

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

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

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