alleryIf $f(x)$ is continuous and $\displaystyle\int_0^x f(t)\, dt = x^2(1 + x)$, then $f(2) = ?$
A$8$
B$12$
C$16$
D$24$
Answer & Solution
Correct answer: C. $16$
By FTC, $f(x) = \dfrac{d}{dx}[x^2(1+x)] = \dfrac{d}{dx}(x^2 + x^3) = 2x + 3x^2$. $f(2) = 4 + 12 = 16$.
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