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

`int_(-(3pi)/2)^(-pi/2) {(pi+x)^3+cos^2(x+3pi)}dx` is equal to (A) `pi/4-1` (B) `pi^4/32` (C) `pi^4/32+pi/2` (D) `pi/2`

A

`(pi^(4))/32`

B

`(pi^(4))/32+(pi)/2`

C

`(pi)/2`

D

`(pi)/4-1`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
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  2. If f(x)={(e^(cosx)sinx, |x|le2),(2, otherwise):} then int-2^3f(x)dx= (...

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  3. int(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dxi se q u a lto -4 (b) 0 (c...

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  4. If f(x) is defined on [-2, 2] by f(x) = 4x^2 – 3x + 1 and g(x) = (f(-x...

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  5. int-2^2 |x| dx is equal to

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  6. int(-2)^(2)|xcos pix|dx is equal to

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  7. int(0)^(1) x tan^(-1) x " "dx =

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  8. int(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=

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  9. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x)) dx is

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  10. Evaluate: int(-1)^1(sinx-x^2)/(3-|x|)dx

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  11. The value of integral overset(pi)underset(-pi)int (cos ax-sin b x)^(2)...

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  12. int(-(3pi)/2)^(-pi/2) {(pi+x)^3+cos^2(x+3pi)}dx is equal to (A) pi/4-1...

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  13. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  14. Evaluate: int(pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx

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  15. Let p(x) be a function defined on R such that underset(xrarr infty)(l...

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  16. A(x)=|(1,2,3),(x+1,2x+1,3x+1),(x^(2)+1,2x^(2)+1,3x^(2)+1)|impliesint(0...

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  17. The value of int 0^(sin^2x)sin^(-1)sqrt(t)dt+int 0^(cos^2x)cos^(-1)sqr...

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  18. If M=int(0)^((pi)/2)(cosx)/(x+2)dx and N=int(0)^((pi)/4)(sinxcosx)/((x...

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  19. If for nonzero x ,af(x)+bf(1/x)=1/x-5, where a!=b then int1^2f(x)dx=1

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  20. Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin...

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