Chapter 20 Multiple choice questions

* not completed

. Separate the variables and integrate the following:
$\frac{\text{d}y}{\text{d}x}=y^2{x}^3$.

$\frac{1}{3y^2}=\frac{-x^4}{4}+c$ correct incorrect

$\frac{1}{y}=\frac{-x^4}{4}+c$ correct incorrect

$y=\frac{y^2{x}^4}{4}+c$ correct incorrect

$y=\frac{y^3{x}^4}{12}+c$ correct incorrect

* not completed

. Separate the variables and integrate the following:
$\frac{\text{d}h}{\text{d}t}={\text{e}}^{2h}{t}^4$.

$c=\frac{{\text{e}}^{2h}{t}^5}{10}$ correct incorrect

${\text{e}}^{-2h}=\frac{-2t^5}{5}+c$ correct incorrect

$h=\frac{{\text{e}}^{2h}{t}^5}{5}+c$ correct incorrect

${\text{e}}^{2h}=\frac{2t^5}{5}+c$ correct incorrect

* not completed

. Separate the variables and integrate the following:
$\frac{\text{d}p}{\text{d}q}=p\sin q$.

$-2=p\cos q+c$ correct incorrect

$1=p^2\cos q+c$ correct incorrect

$p=-\cos q+c$ correct incorrect

$\ln p=-\cos q+c$ correct incorrect

* not completed

. Separate the variables and integrate the following:
$\frac{\text{d}m}{\text{d}p}=\frac{\cos 4p}{\sin 6m}$.

$-6\cos 6m=4\sin 4p+c$ correct incorrect

$6\sin 6m=4\cos 4p+c$ correct incorrect

$-2\cos 6m=3\sin 4p+c$ correct incorrect

$3\cos 6m=-2\sin 4p+c$ correct incorrect

* not completed

. Separate the variables and integrate the following:
$\frac{\sqrt{y^3}}{6x^{2.3}}\frac{\text{d}y}{\text{d}x}=5$.

$\text{6}{\text{.6y}}^{2.5}=150x^{3.3}+c$ correct incorrect

$\text{6}{\text{.6y}}^{2.5}=30x^{3.3}+c$ correct incorrect

$\text{0}{\text{.4y}}^{2.5}=150x^{3.3}+c$ correct incorrect

$\text{0}{\text{.4y}}^{2.5}=30x^{3.3}+c$ correct incorrect

* not completed

. Evaluate the following integral:
$y={\displaystyle {\int }_1^4{x}^5+2x^3-6x^2-10}\text{d}x$.

y = 654 correct incorrect

$y=642\frac{2}{3}$ correct incorrect

$y=-11\frac{1}{3}$ correct incorrect

$y=631\frac{1}{3}$ correct incorrect

* not completed

. Evaluate the following integral:
$y={\displaystyle {\int }_0^3{\text{e}}^{4x}-{\text{e}}^{2x}}\text{d}x$.

$y=\frac{1}{4}{\text{e}}^{12}-\frac{1}{2}{\text{e}}^6-\frac{1}{4}$ correct incorrect

$y=\frac{1}{4}{\text{e}}^{12}+\frac{1}{2}{\text{e}}^6-\frac{1}{4}$ correct incorrect

$y=-\frac{1}{4}{\text{e}}^{12}-\frac{1}{2}{\text{e}}^6+\frac{1}{4}$ correct incorrect

$y=\frac{1}{4}\left({\text{e}}^{12}-2{\text{e}}^6+1\right)$ correct incorrect

* not completed

. Evaluate the following integral:
$y={\displaystyle {\int }_0^{\frac{\pi }{2}}\frac{\cos 3x}{4}}\text{d}x$.

y = -1 correct incorrect

$y=\frac{-3}{4}$ correct incorrect

$y=\frac{-1}{12}$ correct incorrect

$y=\frac{3}{4}$ correct incorrect

* not completed

. Evaluate the following integral:
$y={\displaystyle {\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}\frac{\sin 4x}{8}}\text{d}x$.

$y=\frac{-1}{16}$ correct incorrect

$y=\frac{1}{16}$ correct incorrect

$y=\frac{-1}{32}$ correct incorrect

$y=0$ correct incorrect

* not completed

. Evaluate the following integral:
$y={\displaystyle {\int }_1^{{\text{e}}^3}\frac{5}{x}}\text{d}x$.

$y=5\ln 3$ correct incorrect

$y=15$ correct incorrect

$y=5{\text{e}}^{-3}-5$ correct incorrect

$y=15{\text{e}}^{-3}-5$ correct incorrect