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

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

int_(0)^(4)(x+e^(2x))dx

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

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)^(2)(x+2)/(x+1)dx is

int_(2)^(0) x(2-x)^4 dx

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

int_(0)^(4) |x-1|dx

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta