Question

If $k_1\le \underset{1}{\overset{2}{\int }}{e}^{(x^3+x)}dx\le k_2$, then

• A. $k_1=e^3$
• B. $k^2=e^{10}$
• C. $k_1=e^2$
• D. $k^2=e^{11}$

Answer 1

Answer: (B), (C)

$k_1=e^2$

$e^{(x^3+x)}$ is increasing function in $(1,2)$
Minimum value $=e^2$
Maximum value $=e^{10}$
$\Rightarrow k_1=e^2(2–1)=e^2$
$k_2=e^{10}(2–1)=e^{10}$