`int_0^2{x}^([x])dx`

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^1 2^(x-[x])dx

Evaluate the following integrals : int_0^2(x^2+x)dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^2x[x]dx

Evaluate the following definite integrals as limit of sums. int_0^4(x+e^(2x))dx

prove it 2e^(-1/4) < int_0^2e^(x^2-x)dx < 2e^2

Evaluate: lim_(x->oo)((int_0^xe^(x^2)dx)^2)/(int_0^x e^(2x^2)dx)

If y=f(x) makes positive intercepts of 2 and 1 unit on x and y-coordinates axes and encloses an area of 3/4 sq unit with the axes, then int_0^2 x f'(x)\ dx , is

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

1) int_(-pi/2)^pi sin^(-1) (sinx) dx 2) int_(-pi/2)^(pi/2) (-pi/2)/(sqrt(cos x sin^2 x)) dx 3) int_0^2 2x[x] dx