Integration and Accumulation of Change

Let $g(x) = \int_{x}^{x^2} f(t) dt$. Find $g'(x)$.

Find the value of $\int_{0}^{1} e^x dx$.

Given $g(x) = \int_{0}^{x} (t^2 + 1) dt$, find $g'(x)$.

If $g(x) = \int_{1}^{x^2} t^3 dt$, find $g'(x)$.

If $g(x) = \int_{2}^{x} t^3 dt$, find $g'(x)$.

Evaluate the definite integral $\int_{1}^{3} x^2 dx$ using the Fundamental Theorem of Calculus Part 2.

Using u-substitution and the Fundamental Theorem of Calculus Part 2, evaluate $\int_{0}^{2} x\sqrt{4-x^2} dx$.

Evaluate $\int_{0}^{\pi/4} \tan^2(x) dx$.

Find $g'(x)$ if $g(x) = \int_{0}^{x^2} t^4 dt$.

If $g(x) = \int_{\sin(x)}^{x^3} t^2 dt$, find $g'(x)$.