Question

If ${\int }_0^1\left(3x^2+5x+k\right)dx=0$ find $k$.

Answer 1

Given,

${\int }_0^1\left(3x^2+5x+k\right)dx=0$

or, $[x^3{]}_0^1+\frac{5}{2}[x^2{]}_0^1+k[x{]}_0^1=0$

or, $1+\frac{5}{2}+k=0$

or, $k=-\frac{7}{2}$.