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If int(0)^(x)f(t)dt = x^(2)-int(0)^(x^(2...

If `int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt` then find `f(1)`.

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. If f(x) = int(0)^(x^(2)) sqrt(cost)dt, find f'(x)

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

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  3. If int(0)^(x)f(t)dt = x^(2)-int(0)^(x^(2))(f(t))/(t)dt then find f(1).

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  4. If f(x) = int(x)^(x^(2)) t^(2)lnt then find f'(e)

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  5. If y = int(4)^(4x^(2))t^(4)e^(4t)dt, find (d^(2)y)/(dx^(2))

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  6. If y = int(0)^(x^(2))ln(1+t), then find (d^(2)y)/(dx^(2))

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  7. If int(0)^(x^(2)(1+x))f(t)dt = x then find f(2)

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  8. Evaluate int(0)^(pi)ln(1+bcosx) dx, 'b' being parameter.

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  9. int(pi//2)^(0)sin^(11)xdx

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  10. int(0)^(-pi//2)sin^(5)xcos^(4)xdx

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  11. int(0)^(1) x^(5)sin^(-1)xdx

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  12. int(0)^(9) x(a^(2)-x^(2))^(7/2)dx

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  13. int(0)^(2) sqrt(2-x)dx.

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  14. Prove the following : int(0)^(1)e^(-x)cos^(2)xdx lt int(0)^(1)e^(-x^(2...

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  15. Prove the following : 0 lt int(0)^(pi//2)sin^(n+1)xdx lt int(0)^(pi//2...

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  16. Prove the following : e^(-(1)/(e)) lt int(0)^(1)x^(x)dx lt 1

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  17. Prove the following: -1/2lt=int0^1(x^3cosx)/(2+x^2)dx<1/2

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  18. Prove the following : 1 lt int(0)^(pi//2)sqrt(sinx)dx lt sqrt(pi/2)

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  19. Prove the following : 4/pi lt int(pi/4)^(pi/3) (tanx)/(x) lt (3sqrt(3)...

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  20. lim(nrarroo) {1/n+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+"......"+1/(...

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