Question

If $\underset{0}{\overset{1}{\int }}\left(3x^2+2x+k\right)dx=0,$ find the value of k.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ {\int }_0^1\left(3x^2+2x+k\right)dx=0 \\ \Rightarrow {\left[x^3+x^2+kx\right]}_0^1=0 \\ \Rightarrow 1+1+k-0=0 \\ \Rightarrow k=-2 \end{gathered}$$. →