If $\int\limits_0^1\left(3 x^2+2 x+5 k\right) d x=0$, then the value of k is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - $-\frac{2}{5}$
$\int\limits_0^1\left(3 x^2+2 x+5 k\right) d x=0$
$⇒\left[x^3+x^2+5kx\right]_0^1=0$
$⇒1+1+5k=0⇒k=-\frac{2}{5}$