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

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

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

Evaluate int_(0)^(2)(x^(2)+2x+1)dx as limit of a sum.

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

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

int_(0)^(1)(2-x^(2))/(1+x^(2))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^(2))dx then

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

int_(0)^(12)(2x)dx-1=

The value of int_(0)^(oo)(dx)/(1+x^(4)) is (a) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x) (b) (pi)/(2sqrt(2))( c) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x^(4))(d)(pi)/(sqrt(2))