in exercises 1 - 20, find $dy/dx$.\n1. $y=int_{0}^{x}(sin^{2}t)dt$

Explanation:

Step1: Apply the fundamental theorem of calculus

According to the fundamental theorem of calculus, if $y=\int_{a}^{x}f(t)dt$, then $\frac{dy}{dx}=f(x)$. Here, $a = 0$ and $f(t)=\sin^{2}t$.

Step2: Find the derivative

Since $f(t)=\sin^{2}t$, when we find $\frac{dy}{dx}$, we substitute $x$ for $t$ in $f(t)$. So $\frac{dy}{dx}=\sin^{2}x$.

Answer:

$\sin^{2}x$