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Let I= int(0)^(pi//2) (dx)/(1+sin x') th...

Let `I= int_(0)^(pi//2) (dx)/(1+sin x')` then `int_(0)^(pi) (x^(2) cos x)/((1+ sin x)^(2)) dx`

A

`-pi^(2)`

B

`pi^(2)- 2pi I`

C

`2pi I`

D

`2pi I- pi^(2)`

Text Solution

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The correct Answer is:
D
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ML KHANNA-DEFINITE INTEGRAL-ProblemSet (2) (Multiple Choice Questions)
  1. int(0)^(pi) x f (sin x)dx=

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  2. Evaluate int0 ^oo log(x+1/x) dx / (1+x^2)

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  3. int(0)^(pi//2) [2log sin x-log sin 2x] dx=

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  4. If int(0)^(pi) x f(sin x)dx= k int(0)^(pi//2) f(sin x) dx then the val...

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  5. For n gt 0 int(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

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  6. int(0)^(pi//2) (sin^(2)x)/(sin x+cos x) dx is equal to

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  7. The value of the integral int(0)^(1) x (1-x)^(n) dx is

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  8. If int(0)^(1) x^(m) (1-x)^(n) dx= R int(0)^(1) x^(n) (1-x)^(m) dx, the...

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  9. If I= int(0)^(1) (e^(t))/(1+t) dt, then p= int(0)^(1) e^(t) log (1+t) ...

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  10. int(0)^(pi//2n) (dx)/(1+ cot^(n) nx) is equal to

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  11. The value of the integral underset(0)overset(1)int cot^(-1) (1-x+x^...

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  12. int(0)^(1) tan^(-1) (1-x+x^(2)) dx=

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  13. int(0)^(pi//2) (cos x dx)/(1+ cos x +sin x)=

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  14. Let I= int(0)^(pi//2) (dx)/(1+sin x') then int(0)^(pi) (x^(2) cos x)/(...

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  15. a(n) = int(0)^(pi//2) (sin^(2) nx)/(sin x)dx, then a(2)-a(1), a(3)-a(2...

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  16. If f(x) and g(x) are continuous functions satisfying f(x)= f(a-x) and ...

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  17. If f (x) is monotonic differentiable function on [a,b] then int(a)^(b)...

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  18. Let T >0 be a fixed real number. Suppose f is continuous function such...

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  19. If lim(t to a) (int(a)^(t) f(t)dt-(t-a)/2 (f(t) -f(a)))/(t-a)^(3)= 0, ...

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  20. If f(y)= e^(y), g(y)= y, y gt 0 and F(t) = int(0)^(t) f(t-y) g(y) dy, ...

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