Question

question 4 (1 point)
let $g(x)=\int_{2}^{x}\sin(t)e^{t}dt$. then $g(x)$ equals
$\sin(x)e^{x}-\sin(2)e^{2}$
$\sin(x)e^{x}$
$\cos(x)e^{x}+\sin(x)e^{x}$
$\sin(t)e^{t}$
none of these options are correct.
view hint for question 4

Explanation:

Step1: Apply Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus Part 1 states that if \( g(x) = \int_{a}^{x} f(t)dt \), then \( g'(x) = f(x) \). Here, \( f(t) = \sin(t)e^t \) and the lower limit is a constant (2), so the derivative of the integral with respect to \( x \) is just \( f(x) \).

Answer:

sin(x)e^x