Find `int_(-1)^(1) |x| dx`.

Find int_(-1)^(1) x^(3) e^(2) dx.

If f is an even function and g is an odd function defined on [-1,1] find int_(-1)^(1) f(x) g (x) dx.

Evaluate int_(-2)^(4) |x-1| dx.

Evaluate int_(0)^(1) [x] dx.

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x) dx . Hence, evaluate int_(0)^(pi//2) (sin x - cos x)/(1+ sin x cos x) dx.

Evaluate int_(1)^(4) f(x) dx, where f(x)={{:(4x+3",",1 le x le 2),(3x+5",",2 le x le 4):}

Evaluate int_(0)^(pi//4) sin 2x dx

Evaluate the integrals int(x^8-1)/(x-1) dx