If \(\int_{0}^{1}\displaystyle\left(3x^{2}+2kx+1\right)dx = 5\), then the value of k is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
Integrating term by term, with k a constant:
\( \displaystyle \int_{0}^{1}\left(3x^{2}+2kx+1\right)dx = \left[x^{3} + kx^{2} + x\right]_{0}^{1} \)
\( = 1 + k + 1 = k + 2 \)
Setting this equal to 5:
\( k + 2 = 5 \)
\( k = 3 \)