Question

if $f(x) = \int_{0}^{x} (t^3 + 4t^2 + 7) dt$ then $f(x) = $

Explanation:

Step1: Apply Fundamental Theorem of Calculus

$f'(x) = x^3 + 4x^2 + 7$

Step2: Differentiate $f'(x)$ to get $f''(x)$

$f''(x) = \frac{d}{dx}(x^3 + 4x^2 + 7) = 3x^2 + 8x$

Answer:

$3x^2 + 8x$