The value of \(\int_{1}^{3}\displaystyle (3x^{2} - 2x)\,dx\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 18
An antiderivative of \(3x^{2} - 2x\) is \(x^{3} - x^{2}\). By the fundamental theorem of calculus,
\( \displaystyle \int_{1}^{3}(3x^{2} - 2x)\,dx = \Big[x^{3} - x^{2}\Big]_{1}^{3} \)
\( = (27 - 9) - (1 - 1) \)
\( = 18 \)