AP Calculus ABmediummcq1 pt

What is the area of the region enclosed by the graphs of $y=\sqrt{x}$ and $y=\frac{x}{4}$ ?

\frac{128}{3}

32

\frac{32}{3}

\frac{64}{3}

Explanation

Core Concept

The curves intersect at $x=0$ and $x=16$ . The area is $\int_0^{16}(\sqrt{x}-\frac{x}{4})\,dx=[\frac{2}{3}x^{3/2}-\frac{x^2}{8}]_0^{16}=\frac{128}{3}-32=\frac{32}{3}$ .

Correct Answer

C $\frac{32}{3}$

More Unit 8: Applications of Integration practice questions

hardThe base of a solid is the region bounded by the graphs of $x=y^2$ and $x=4$. Cross sections perpendicular to the $y$-axis are squares. What…
hardThe base of a solid is the region in the first quadrant bounded by the graph of $y=x^2$, the $x$-axis, and the line $x=2$. Cross sections pe…
hardThe base of a solid is the region bounded by the graph of $y=x^2$ and the line $y=4$. Cross sections perpendicular to the $y$-axis are squar…
hardThe base of a solid is the region bounded by the graph of $y=1-x^2$ and the $x$-axis. Cross sections perpendicular to the $x$-axis are equil…
mediumThe base of a solid is the region bounded by the graph of $y=1-x^2$ and the $x$-axis. Cross sections perpendicular to the $x$-axis are semic…

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 8: Applications of Integration Questions →

What is the area of the region enclosed by the graphs of y=xy=\sqrt{x}y=x​ and y=x4y=\frac{x}{4}y=4x​?

Explanation

Core Concept

Correct Answer

More Unit 8: Applications of Integration practice questions

What is the area of the region enclosed by the graphs of $y=\sqrt{x}$ and $y=\frac{x}{4}$ ?