Areas (College Board AP® Calculus AB): Exam Questions

If $0\le k<\pi$ and the area under the curve $y=\sin x$ from $x=0$ to $x=k$ is 1.2, then $k=$

The function $f$ is defined by $f\left(x\right)=\{\begin{array}{l}5-x\mathrm{for}x\le 2\\ 3\mathrm{for}x>2\end{array}$. What is the value of ${\int }_{-1}^{6}f\left(x\right)dx$?

The area of the region enclosed by the graph of $y=x^2-2x+1$ and the graph of $y=x+1$ is

Which one option out of the following does not represent the total shaded area shown above?

The area of the shaded region between $y=\frac{1}{2}\ln \left(\frac{x-5}{4}\right)$ and the $y$-axis, shown above, is

Let $R$ be the region bounded by the graph of $x=\ln y$, the vertical line $x=1$, and the horizontal lines $y=e$ and $y=5$. Which of the following gives the area of $R$?

What is the area of the region between the graphs of $y=\sqrt{x}$ and $y=-x$ from $x=0$ to $x=4$?

Which of the following integrals represents the area of the shaded region in the figure above?

What is the total area enclosed between the curve $y=x^3-8x^2+21x-13$ and the line $y=2x-1$?

The regions P, Q and R are bounded by the curve $x=f\left(y\right)$ and the $y$-axis. If the area of each region is 6, what is the value of ${\int }_{-1}^2\left(f\left(y\right)+5\right)dy$?