MCQ
The value of $\int\limits_0^1 {{e^{{e^x}}}} \left( {1 + x.{e^x}} \right)dx$ is
- A$e$
- ✓$e^e$
- C$e^e -e$
- D$e^e -1$
$I = \int_1^e {{e^t}} \left( {\frac{{1 + t\ln t)}}{t}} \right)dt = \int_1^e {{e^t}} \left( {\ln t + \frac{1}{t}} \right)dt = {e^e}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x)=\left\{\begin{array}{rc}x^5+5 x^4+10 x^3+10 x^2+3 x+1, & x<0 \\ x^2-x+1, & 0 \leq x<1 \\ \frac{2}{3} x^3-4 x^2+7 x-\frac{8}{3}, & 1 \leq x<3 \\ (x-2) \log _e(x-2)-x+\frac{10}{3}, & x \geq 3\end{array}\right.$
Then which of the following options is/are correct?
$(1)$ $f^{\prime}$ has a local maximum at $x =1$ $(2)$ $f$ is onto
$(3)$ $f$ is increasing on $(-\infty, 0)$ $(4)$ $f^{\prime}$ is $NOT$ differentiable at $x =1$