int_(a)^(b)x^(5)dx

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If int_(a)^(b)x^(3)dx=0, and If int_(a)^(b)x^(2)dx=(2)/(3), find a and b.

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If f(a+b-x)=f(x), then prove that int_(a)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx

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int_(a)^(b)f(x)dx=int_(b)^(a)f(x)dx .

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If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a

int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx. Hence evaluate : int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx.

Prove that int_(a)^(b)(x)dx = int_(a)^(b)f(a+b-x)dx and int_(pi/4)^(pi/3)(dx)/(1+sqrt(tanx)) .