question\ngiven $f(x)$ below, find $f(x)$.\n$f(x)=int_{2}^{x}e^{t^{3}+14}dt$\nprovide your answer…
question\ngiven $f(x)$ below, find $f(x)$.\n$f(x)=int_{2}^{x}e^{t^{3}+14}dt$\nprovide your answer below:\n$f(x)=square$
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, $a = 2$ and $f(t)=e^{t^{3}+14}$.
Step2: Find the derivative
By the fundamental theorem of calculus, for $F(x)=\int_{2}^{x}e^{t^{3}+14}dt$, we have $F^{\prime}(x)=e^{x^{3}+14}$.
Answer:
$e^{x^{3}+14}$