If \(\int_{0}^{a}\displaystyle 3x^2\,dx = 8\), then the value of \(a\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2
Since \(\frac{d}{dx}(x^3) = 3x^2\), by the fundamental theorem of calculus
\(\displaystyle \int_{0}^{a} 3x^2\,dx = \Big[x^3\Big]_{0}^{a} = a^3\)
\(a^3 = 8\)
\(a = 2\)