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Evaluate the following definite integral...

Evaluate the following definite integral: `int_(-pi)^(pi)(2x(1+sinx))/(1+cos^(2)x)dx`

A

`pi^(2)//4`

B

`pi^(2)`

C

0

D

`pi//2`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. If I(mn)=int(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m, n epsilon I, m,n ge 0 ), t...

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  2. Find the points of maxima /minima of int(0)^(x^(2))(t^(2)-5t+4)/(2+e^(...

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  3. Evaluate the following definite integral: int(-pi)^(pi)(2x(1+sinx))/(1...

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  4. The value of the inntegral int(alpha)^(beta) (1)/(sqrt((x-alpha)(beta-...

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  5. The value of the integral int(alpha)^(beta) sqrt((x-alpha)(beta-x))dx,...

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  6. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

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  7. The value of integral int(1)^(e) (log x)^(3)dx , is

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  8. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  9. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  10. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

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  11. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

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  12. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

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  13. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

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  14. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

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  15. Let I= int(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral ...

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  16. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  17. int(pi)^(10n) |sin x|dx is equla to

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  18. about to only mathematics

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  19. If int(0)^(oo)e^(-ax)dx=(1)/(a)," then "int(0)^(oo)x^(n)e^(-ax)dx is

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  20. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

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