If f(x)=`int e^(x)(x-1)(x-2)dx`, then show that f(x) is a decreasing function `1 lt x lt 2`.

Let f(x)=inte^x(x-1)(x-2)dx , then f(x) decreases in the interval

If f'(x) exists and if f'(x) lt 0 everywhere in the interval a le x le b , then show that f(x) is a decreasing function in a le x lt b .

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

If f(2a-x)=-f(x) , then show that, int_(0)^(2a)f(x)dx=0

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c , then (a) f(x) is an even function (b) f(x) is a bounded function (c) the range of f(x) is (0,1) (d) f(x) has two points of extrema

Prove that the function f(x)=x^(3)-x^(2) is neither increasing nor decreasing in -2/3 lt x lt 2/3 .

If f(x)=log_e.(1+x)/(1-x) , show that f((2x)/(1+x^2))=2f(x) .

If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric function for |a|>2 f(x) is logarithmic function for |a| 2 g(x) is rational function for |a|<2

If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).

A function f(x) is defined in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-