`int_a^bx^2dx`

If int_a^b x^3dx=0 , and If int_a^b x^2dx=2/3, find a and b.

Evaluate int_a^b x^2 dx as limit of the sum.

Evaluate: int_1^2x^2dx

STATEMENT 1: int_0^pixsinxcos^2xdx=pi/2int_0^pisinxcos^2x dx . STATEMENT 2: int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx .

int_1^4 3x^2dx

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

Evaluate int_0^2e^2dx

int(ax^3+bx^2+cx+d)dx

int_a^b logx/x^2dx

If f is an integrable function, show that int_(-a)^af(x^2)dx=2int_0^af(x^2)dx