Question

If ${\int }_1^a(3x^2+2x+1)dx=11$, find $a$.

Answer 1

Given,

$\begin{array}{c}{\int }_1^a\left(3x^2+2x+1\right)dx=11\\ \Rightarrow {\left[x^3+x^2+x\right]}_1^a=11\\ \Rightarrow a^3+a^2+z=14\\ \Rightarrow \left(a-2\right)\left(a^2+3a+7\right)=0\\ \Rightarrow a=2\end{array}$

Hence,

We get $a=2$.