`int_(0)^(2)(x^(4)-3x^(2)-1)dx`

The value of (int_(0)^(2)x^(4)sqrt(4-x^(2))dx)/(int_(0)^(2)x^(2)sqrt(4-x^(2)dx) is equal to

int_(0)^(2) (1)/(4+x+x^(2))dx

Evaluate the following definite integrals. (a) int_(0)^(3)(x^(2)+1)dx (b) int_(2)^(3)(x^(3)-4x^(2)+5x-10)dx (c) int_(0)^(pi//4)(cosx-sinx)dx

int_(0)^(3)(x^(2)+1)dx

1. int_(0)^(2)3x^(2)dx

int_(0)^(1)(2x)/((1+x^(4)))dx

Evaluate : int_(0)^(4) x(4-x)^(3//2)dx

int_0^2(3x^2-4)dx

(3) (a) int_(0)^(2)(x^(4)+1)dx

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then