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int ( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ c...

`int _( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ cos ^(2) x )`

A

`pi ^(2) `

B

`pi ^(2) //4`

C

`pi//8`

D

`pi ^(2) //8`

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The correct Answer is:
A
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. int (-1) ^(1) (sin x + x ^(2))/( 3 - |x|) dx

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  2. The value of overset(pi//4)underset(-pi//4)int(e^(x)sec^(2)x)/(e^(2x)-...

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  3. int ( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ cos ^(2) x )

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  4. int (0) ^(pi) (cos ^(2) x ) dx,

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  5. If int0^11 (11^x)/(11^([x])) dx=k/(log 11) then value of k is (where [...

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  6. Let Tgt0 be a fixed real number. Suppose f is a cintinuous function s...

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  7. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

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  8. The value of lim(xto0) (int(0)^(x^2)sec^2t dt)/(x sin x) dx , is

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  9. underset( x to 0) lim ( int(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

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  10. If int0^y cos t^2\ dt = int0^(x^2)\ sint/t \ dt, then dy/dx is equal t...

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  11. let f(x)=int(t^2-t+1)dt,AA x in (3,4), then the difference between th...

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  12. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

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  13. The smallest interval [a,b] such that overset(1)underset(0)int (1)/...

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  14. Given that n is odd and m is even integer. the value of int (0) ^(x ) ...

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  15. underset(n to oo)"lim"underset(r=1)overset(n)sum((r^(3))/(r^(4) + n^(4...

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  16. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

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  17. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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  18. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  19. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

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  20. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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