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Prove that: int0^(2pi)(xsin^(2n)x)/(s...

Prove that: `int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx`

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BANSAL-INTEGRALS-All Questions
  1. Find value of following definite integrals: int(-pi/4)^(npi-pi/4)|s...

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  2. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

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  3. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

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  4. Evaluate : int1^16tan^(- 1)sqrt(sqrt(x)-1)dx

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  5. Let f(x)=\ int1^xsqrt(2-t^2)dtdot Then the real roots of the equati...

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  6. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  7. The tangent int(-1/2)^(1/2)([x]+ln((1+x)/(1-x)))\ dx equals, where [\ ...

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  8. int0^pisqrt((1-x)/(1+x))dx= (pi^)/2 (b) (pi^)/2-1 (c) (pi^)/2+1...

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  9. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  10. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  11. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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  12. If int(sinx)^1 t^2f(t)dt=1-sinx, then the value of f(1/sqrt(3)) is (A)...

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  13. 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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  14. Evaluate: int0^pie^(cos x)(2sin(1/2cos x)+cos(1/2cos x))sinx dxdot

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  15. Evaluate : int(0)^(pi//2) sin x dx

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  16. For every function f (x) which is twice differentiable , these will be...

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  17. If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x...

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  18. Find the value of (5050int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^...

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  19. (lim)(x->4)(int2sec^2\ f(t)dt)/(x^2-(pi^2)/(16)) equals a.8/pif(2) b. ...

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  20. int(-1)^1(dx)/(1+x^2)

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