Chapter 22 Multiple choice questions

* not completed

. Determine the area bounded by:
The x-axis, the curve $y=2x^2+x-6$, and the lines x = 4 and x = 6.

298 correct incorrect

$99\frac{1}{3}$ correct incorrect

126 correct incorrect

$26\frac{2}{3}$ correct incorrect

* not completed

. Determine the area bounded by:
The x-axis, the curve $y=\frac{2}{x^3}$, and the lines x = 0.25 and x = 1.

-62 correct incorrect

1 correct incorrect

16 correct incorrect

15 correct incorrect

* not completed

. Determine the area bounded by:
The x-axis, the curve y = 5x² + 5x - 30, and the lines x = −4 and x = 2.

$118\frac{1}{3}$ correct incorrect

90 correct incorrect

$14\frac{1}{6}$ correct incorrect

$104\frac{1}{6}$ correct incorrect

* not completed

. Determine the area bounded by:
The x-axis, the curve y = sin 2x, and the lines x = $\frac{\pi }{4}$, and x = $\frac{3\pi }{4}$.

0.5 correct incorrect

1 correct incorrect

0.25 correct incorrect

1.5 correct incorrect

* not completed

. Determine the volume formed by rotating $y^2=\frac{x}{4}$ about the x-axis between x = 5 and x = 10.

$\frac{75}{8}$ correct incorrect

$\frac{125}{8}$ correct incorrect

$\frac{75}{8}\pi$ correct incorrect

$\frac{125}{8}\pi$ correct incorrect

* not completed

. Determine the volume formed by rotating $y=\sqrt{x^3}$ about the x-axis between x = 4 and x = 6.

$260\pi$ correct incorrect

260 correct incorrect

$22.5\pi$ correct incorrect

22.5 correct incorrect

* not completed

. Determine the volume formed by rotating y = 5x² about the y-axis between x = 2 and x = 3.

$\frac{325\pi }{2}$ correct incorrect

$\frac{325}{2}$ correct incorrect

$\frac{1}{2}$ correct incorrect

$\frac{\pi }{2}$ correct incorrect

* not completed

. Calculate the following: ${\displaystyle {\int }_0^1{\displaystyle {\int }_1^2{\displaystyle {\int }_2^3\left(xyz+x^3{y}^2\right)}}}\text{d}z\text{d}y\text{d}x$.

$\frac{73}{12}$ correct incorrect

$\frac{59}{24}$ correct incorrect

$\frac{9}{4}$ correct incorrect

$\frac{191}{72}$ correct incorrect

* not completed

. Calculate the following: ${\displaystyle {\int }_0^1{\displaystyle {\int }_0^x{\displaystyle {\int }_0^{y-2}\left(x^{3}yz\right)\text{d}z\text{d}y\text{d}x}}}$.

$\frac{39}{448}$ correct incorrect

$\frac{11}{24}$ correct incorrect

$\frac{1}{2}$ correct incorrect

$\frac{1}{64}$ correct incorrect

* not completed

. Calculate the following:
${\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_0^{\pi }{\displaystyle {\int }_0^{\infty }f\left(r,\theta ,\varphi \right)r^2\sin \theta \text{d}r\text{d}\theta \text{d}\varphi }}}$,
where $f\left(r,\theta ,\varphi \right)=r^3\exp \left(-4r^2\right)$.

$\frac{\pi }{64}$ correct incorrect

$\frac{\pi }{32}$ correct incorrect

$\frac{\pi }{16}$ correct incorrect

$\frac{\pi }{8}$ correct incorrect