Sample test $5$ v $\mathrm{.}2$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(7x^5-5x^4-{}^3{e}^x-3)dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x^3-3x^4{x}^3-3x^{2}3x}{x^3}dx=$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{5}{2}-\frac{3x}{5})dx=$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(cs{c}^{2}a-cosx-sectan)d=$

$f^{\text{'}}(x)=7x\frac{1}{e^4}-x^3$ find $f(x)$ if $f(0)=7$

${\displaystyle \underset{k=1}{\overset{37}{}}}(3k^{3}2k^2-6k5)$

${\displaystyle \underset{k=1}{\overset{n}{}}}(\frac{2k-3}{n^3}{)}^2\frac{1}{n^2}$

Find the position at the time $t=3$ seconds of a particle if $v(t)=7t-2$;$s=5$ when $t=1.$

Given that the graph of $f$ passes through the point $(5,3)$ and that the slope of its tangent at $(x,f(x))$ is $5x-7.$ Find $f(-5).$

Find a function $f$ such that $f^{\text{'}}(x)=x^3$ and the line $4x-\frac{1}{2}y=3$ is tangent to the graph of $f.$

$11$a$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{7x^2}{\sqrt[3]{13-3x^2}}dx$

$11$b$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2-1}{\sqrt[\phantom{2}]{2x-1}}dx=$

$12.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^3(x^2-5{)}^{35}dx=$

$13.{\displaystyle \underset{-1}{\overset{1}{}}}|4x2|dx$

$14.{\displaystyle \underset{1}{\overset{3}{}}}|-3x1|dx$

$15.{\displaystyle \underset{1}{\overset{0}{}}}\frac{1}{\sqrt[\phantom{2}]{x}(1\sqrt[\phantom{2}]{2}{)}^5}dx=$

$16.{\displaystyle \underset{2}{\overset{3}{}}}3x^4{e}^{x^3}dx=$

$17.\frac{1}{dx}{\displaystyle \underset{2e}{\overset{x^3}{}}}{t}^2{e}^{t^b}dt=$

$18.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{14}{\sqrt[\phantom{2}]{7-6x^2}}dx$

$19.{\displaystyle \underset{\frac{1}{3}}{\overset{\frac{4}{3}}{}}}\frac{x}{3}sin5xdx$

$20.{\displaystyle \underset{0}{\overset{\frac{}{12}}{}}}(1-co{s}^{2}4t)cos4tdt=$

$21.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cosx}{1si{n}^{2}x}dx=$

$22.$ Find the area of the region bounded by the graphs of $y=x^2-4x3$ and $y=-x^{2}2x3.$

$23.$ Find the area of the region bounded by the graphs of $y=\sqrt[\phantom{2}]{x}3$ and $y=\frac{1}{2}x3.$

$24.$ Find the area of the region bounded by the graphs of $x=3-y^2$ and $x=y1.$

$25.$ Find the area of the region bounded by the graphs of $y=\frac{10}{x},x=0,y=2$ and $y=10.$

Bonus: The horizontal line $y=c$ intersects the curve $y=2x-3x^3$ in the first quadrant. Find $c$ so that the area of the two bounded regions are equal.