AP Calculus AB Unit 6: Integration and Accumulation of Change

Find the average value of $f(x)=x^2$ on $[0,3]$.

If $F(x)={\int }_0^x{t}^{3}dt$, what is $F^{\prime }(x)$?

If a particle has velocity $v(t)=3t^2-6t$ (m/s), what is its displacement from $t=0$ to $t=4$?

Use a left Riemann sum with 4 equal subintervals to approximate ${\int }_0^4{x}^{2}dx$.

Evaluate ${\int }_0^2(x^2+1)dx$.

Evaluate $\int (3x^2+4x-5)dx$.

Find $\int x\cos (x^2)dx$.

Evaluate $\int \frac{1}{x}dx$ for $x>0$.