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Evaluate: int0^pie^(cos x)(2sin(1/2cos x...

Evaluate: `int_0^pie^(cos x)(2sin(1/2cos x)+cos(1/2cos x))sinx dxdot`

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

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

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

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

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

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

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

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

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  10. int0^1(dx)/(1-x^2)\

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  11. int2^3(dx)/(1-x^2)

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  12. int1^2(dx)/(x\ sqrt(x^2-1))

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  13. Let f be a non-negative function defined on the interval [0,1]dot If i...

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  14. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

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  15. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

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  16. The value of (lim)(x->0)1/(x^3)int0^x(t ln(1+t))/(t^4+4)dt is a.0 b. 1...

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  17. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

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  18. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  19. For any real number x ,l e t[x] denote the largest integer less than o...

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  20. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

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