Prove that `int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx` and hence evaluate the following:
(e) `int_(0)^(2)xsqrt(2 - x) dx`.

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (d) int_(0)^(1)x(1 -x)^(n)dx .

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (b) int_(0)^(pi/2) cos^(2) xdx .

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (a) int_(0)^(a) (sqrt(x))/(sqrt(x) + sqrt(a) - x)dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (c) int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sin x) + sqrt(cos x))dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (f) int_(0)^(pi)(xdx)/(a^(2)cos^(2)x + b^(2)sin^(2)x)

Prove that int_(0)^(a)(x)dx = int_(0)^(a) f(a-x)dx and hence evaluate int_(0)^(pi/4)log (1 + tan x)dx .

int_(0)^(2)[x^(2)] dx =

Prove that int_(0 )^(a) f (x) dx = int_(0)^(a) f (a -x) dx hence evaluate int_(0)^(pi/2) ( cos^5 x)/( cos^2 x+ sinn ^5 x) dx

Prove that int_(0)^(2a) f(x) dx = 2int_(0)^(a) f(x) dx when f(2a -x) = f(x) and hence evaluate int_(0)^(pi) |cos x| dx .

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .