`int_0^4 x^(1/2) dx `

int_0^4 (2x-1) dx

int_0^1 x^2 e^(2x) dx

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

int_0^1 (x/(x+1))dx

If 2int_0^1 tan^(-1)x dx= int_0^1 cot^(-1)(1-x+x^2) dx then int_0^1 tan^(-1)(1-x+x^2) dx=

IfI_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 ,I_4=int_1^2 2^(x^3)dx , then which of the following is/are true?

If int_0^1e^ (-x^2) dx=a , then find the value of int_0^1x^2e^ (-x^2) dx in terms of a .

int_0^1 x(1-x)^(5/2) dx

Prove that int_0^1tan^(-1)(1/(1-x+x^2))dx=2int_0^1tan^(-1)x dx . Hence or otherwise, evaluate the integral int_0^1tan^(-1)(1-x+x^2)dx

Evaluate: int_0^1 1/(1+x^2)\ dx