simplify the following expression.\n$\frac{d}{dx}int_{4}^{x}(20t^{2}+t + 3)dt$\n$\frac{d}{dx}int_{4}^{x}(20t^…
simplify the following expression.\n$\frac{d}{dx}int_{4}^{x}(20t^{2}+t + 3)dt$\n$\frac{d}{dx}int_{4}^{x}(20t^{2}+t + 3)dt=square$
Answer
Explanation:
Step1: Apply the fundamental theorem of calculus
The fundamental theorem of calculus states that if $F(x)=\int_{a}^{x}f(t)dt$, then $F^\prime(x) = f(x)$. Here, $a = 4$ and $f(t)=20t^{2}+t + 3$.
Step2: Find the derivative
By the fundamental theorem of calculus, $\frac{d}{dx}\int_{4}^{x}(20t^{2}+t + 3)dt=20x^{2}+x + 3$.
Answer:
$20x^{2}+x + 3$