If \( \int_{0}^{1}\displaystyle (4x^{3}+3x^{2}+2x+k)\,dx=0 \), then the value of '\( k \)' is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -3
\( \displaystyle \int_0^1(4x^3+3x^2+2x+k)\,dx=\Big[x^4+x^3+x^2+kx\Big]_0^1 \)
\( \displaystyle =1+1+1+k \)
\( \displaystyle =3+k \)
Since the integral is 0:
\( \displaystyle 3+k=0 \)
\( \displaystyle k=-3 \)