Prove that `0 lt int_0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8`

Prove that pi/6 lt int_0^1(dx) /(sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

Prove that int_(-1)x|x|dx=0

P rov et h a t1/2lt=int_0^(1/2)(dx)/(sqrt(1-x^(2n)))lt=pi/6forngeq1.

Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

Evaluate: int_0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1)

Evaluate int_(0)^(1)x(1-x)^3dx

Prove that int_(0)^(1)log((x)/(x-1))dx=int_(0)^(1)log((x-1)/(x))dx . Find the value of int_(0)^(1)log((x)/(x-1))dx

Prove the following int_(0)^(1)xe^(x)dx=1

Show that : int_0^1(logx)/((1+x))dx=-int_0^1(log(1+x))/x dx