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The tangent, represented by the graph of the function `y=f(x),` at the point with abscissa x = 1 form an angle of `pi//6`, at the point x = 2 form an angle of `pi//3` and at the point x = 3 form and angle of `pi//4`. Then, find the value of,
`int_(1)^(3)f'(x)f''(x)dx+int_(2)^(3)f''(x)dx.`

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - 1
  1. If int0^ooe^(-x^2) dx=(sqrtpi)/2 , then int0^ooe^(-ax^2) dx where ...

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  2. If sum(i=1)^(4)(sin^(-1)x(i)+cos^(-1)y(i))=6pi, then \int\limitsum(i=1...

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  3. The tangent, represented by the graph of the function y=f(x), at the p...

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  4. Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...

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  5. int1^2 x^(2x^2+1)(1+2lnx)dx is equal to

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  6. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  7. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  8. If f(x) = int(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt, f(x+pi) is equal to :

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  9. Let f(x) = int(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x) be the inverse of ...

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  10. Let f(x) is differentiable function satisfying 2int(1)^(2)f(tx) dt ...

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  11. Let I(n) = int(0)^(1)x^(n)(tan^(1)x)dx, n in N, then

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  12. If u(n) = int(0)^(pi/2) x^(n)sinxdx, then the value of u(10) + 90 u(8...

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  13. The value of int(1/e)^(tanx)(tdt)/(1+t^2)+int(1/e)^(cotx)(dt)/(t(1+t^2...

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  14. Let A(1) = int(0)^(x)(int(0)^(u)f(t)dt) dt and A(2) = int(0)^(x)f(u).(...

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  15. The value of underset (nrarrinfty)(lim)("sin"(pi)/(2n)."sin"(2pi)/(2n)...

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  16. Area bounded by the region consisting of points (x,y) satisfying y le ...

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  17. The area enclosed between the curves y=log(e)(x+e),x=log(e)((1)/(y)), ...

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  18. The area enclosed by the curves x=a sin^(3)t and y= a cos^(2)t is equa...

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  19. The area bounded by the curve f(x)=x+sinx and its inverse function bet...

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  20. P(2,2), Q(-2,2) R(-2,-2) & S(2,-2) are vertices of a square. A para...

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