Chapter 19 Multiple choice questions

* not completed

. If $y=a{x}^n$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=\frac{a{x}^{n+1}}{n+1}$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{a{x}^{n-1}}{n-1}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{a{x}^{n+1}}{n}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{a{x}^{n+1}}{n+1}+c$. correct incorrect

* not completed

. If $y=x^6$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=\frac{x^7}{7}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{x^7}{6}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{x^5}{6}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{x^5}{5}+c$. correct incorrect

* not completed

. If $y=\frac{3}{x^4}$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=\frac{15}{x^5}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{-1}{x^3}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{12}{x^3}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\frac{3}{4x^3}+c$. correct incorrect

* not completed

. If $y=6x^{-1}$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=\frac{6}{x^2}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-6x+c$. correct incorrect

${\displaystyle \int y\text{d}x}=\ln 6x+c$. correct incorrect

${\displaystyle \int y\text{d}x}=6\ln x+c$. correct incorrect

* not completed

. If $y=18{\text{e}}^{-3x}$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=6{\text{e}}^{\mathrm{-3}x}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-6{\text{e}}^{3x}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-54{\text{e}}^{-3x}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-6{\text{e}}^{-3x}+c$. correct incorrect

* not completed

. If $y=12x^3-\cos 7x$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=3x^4+\frac{\sin 7x}{7}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=3x^4-\frac{\sin 7x}{7}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=3x^4-7\sin 7x+c$. correct incorrect

${\displaystyle \int y\text{d}x}=3x^4+7\sin 7x+c$. correct incorrect

* not completed

. If $y=15\sin 5x-3{\text{e}}^{9x}$, then ${\displaystyle \int y\text{d}x}=$

${\displaystyle \int y\text{d}x}=3\cos 5x-\frac{{\text{e}}^{9x}}{3}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-75\cos 5x-27{\text{e}}^{9x}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-3\cos 5x-\frac{{\text{e}}^{9x}}{3}+c$. correct incorrect

${\displaystyle \int y\text{d}x}=-3\cos 5x+\frac{{\text{e}}^{9x}}{3}+c$. correct incorrect

* not completed

. Integrate the following differential and determine the constant of integration:
$\frac{\text{d}y}{\text{d}x}=x^5$ which goes through the point (1, 3).

$y=\frac{x^6}{6}+\frac{17}{6}$ correct incorrect

$y=\frac{x^4}{4}+\frac{11}{4}$ correct incorrect

$y=\frac{x^6}{5}+\frac{14}{5}$ correct incorrect

$y=\frac{x^6}{5}+\frac{14}{5}$ correct incorrect

* not completed

. Integrate the following differential and determine the constant of integration:
$\frac{\text{d}y}{\text{d}x}=4{\text{e}}^{8x}$ which goes through the point (1, 7).

$y=32{\text{e}}^{8x}+\left(7-32{\text{e}}^8\right)$ correct incorrect

$y={\text{e}}^{8x}+\left(\frac{7-{\text{e}}^8}{2}\right)$ correct incorrect

$y=16{\text{e}}^{8x}+\left(7-16{\text{e}}^8\right)$ correct incorrect

$y=\frac{{\text{e}}^{8x}}{2}+\left(\frac{\text{14}-{\text{e}}^8}{2}\right)$ correct incorrect

* not completed

. Integrate the following differential and determine the constant of integration:
$\frac{\text{d}y}{\text{d}x}=\frac{8}{x}$ which goes through the point (e⁴, 3).

$y=\frac{8}{x^2}+\left(3-\frac{8}{{\text{e}}^8}\right)$ correct incorrect

$y=\ln 8x+\left(3-4\ln 8\right)$ correct incorrect

$y=8\ln x-29$ correct incorrect

$y=\ln \frac{x}{8}+16$ correct incorrect