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If f(x)=(sinx)/xAAx in (0,pi], prove tha...

If `f(x)=(sinx)/xAAx in (0,pi],` prove that `pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx`

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - II
  1. Evaluate (2005int(0)^(1002)dx(sqrt(1002^(2)-x^(2))+sqrt(1003^(2)-x^(...

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  2. Show that int0^(pi/2)sqrt((sin2theta))sinthetadtheta=pi/4

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  3. Let I(1) = int(0)^(pi//4)1/((1+tanx)^(2))dx, I(2) = int(0)^(1)(dx)/((...

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  4. Find the value of ln(int(0)^(1) e^(t^(2)+t)(2t^(2)+t+1)dt)

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  5. If int(1)^(0) (x)/(x+1+e^(x))dx is equal to -lnk then find the value o...

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  6. If f,f, h be continuous functions on [0,a] such that f(a-x) = f(x), g(...

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  7. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

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  8. Evaluate : 3int(0)^(pi)(a^(2)sin^(2)x+b^(2)cos^(2)x)/(a^(4)sin^(2)x+b^...

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  9. int(0)^(2pi)|sqrt(15) sin x + cos x|dx

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  10. Let a be number in the interval [0,314] such that int(pi+a)^(3pi+a)|x...

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  11. sum(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n) find n

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  12. Iff(x)=x+int0^1t(x+t)f(t)dt , t h e nfin dt h ev a l u eoft h ed efin...

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  13. If f(x) = (ax+b)e^(x) satisfies the equation : f(x) = int(0)^(x)e^(x)"...

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  14. If the minimum of the following function f(x) defined at 0 lt x lt ...

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  15. If f(pi) = 2x^(3)-15x^(2)+24x and g(x) = int(0)^(x)f(t) dt + int(0)^(5...

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  16. Let f(x) = {{:(1-x ,"If" 0 le x le 1),(0, "if" 1 lt x le 2),((2-x)^(2)...

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  17. Find the values of m (m > 0) for which the area bounded by the line y=...

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  18. Find the values of m (m > 0) for which the area bounded by the line y=...

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  19. Find area bounded by y = f^(-1)(x), x = 10, x = 4 and x-axis. Given ...

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  20. Consider a line l: 2x -sqrt(3)y = 0 and a parameterized C :x = tant, y...

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