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If x int(0)^(x)sin(f(t))dx=(x+2)int(0)^(...

If `x int_(0)^(x)sin(f(t))dx=(x+2)int_(0)^(1)tsin(f(t))dt`, where `xgt0`, then show that `f'(x)cot f(x)+3/(1+x)=0`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Suppose f is a real-valued differentiable function defined on [1,oo] ...

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  2. Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) ...

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  3. If x int(0)^(x)sin(f(t))dx=(x+2)int(0)^(1)tsin(f(t))dt, where xgt0, th...

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  4. Evaluate: int0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1]

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  5. I f f(x)=int((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta...

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  6. Find the equation of tangent to the y = F(x) at x = 1, where F(x) = u...

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  7. If int0^x[x]dx=int0^([x])xdx , then prove that either x is purely fr...

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  8. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  9. If I1=int0^1 2^(x^2)dx , I2=int0^1 2^(x^3) dx , I3= int1^2 2^(x^2) dx ...

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  10. If af(x)+bf((1)/(x))=(1)/(x)-5,x ne 0,a ne b, then overset(2)underset(...

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  11. Find the mistake in the following evaluation of the integral I=int0^pi...

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  12. Find the value of int(-1)^1d/(dx)(tan^(-1)(1/x))dx

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  13. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dx is

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  14. The value of int(-2)^2|1-x^2|dx is

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  15. If II=int0^(pi//2)cos(sinx)dx ,I2=int0^(pi/2)sin(cosx)dx \ ,a n d \ I3...

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  16. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  17. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

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  18. value of underset(nrarrinfty)lim((n !)/n^n)^(1/n),where n inN is equal...

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  19. If the value of the definite integral int0^1 "^(207)C7x^(200)(1-x)^7dx...

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  20. Evaluate: int(-1)^0(dx)/(x^2+2x+2)

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