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Here's what students ask on Integrals
Integrals
asked 2021-03-11
A variable force of
\(\displaystyle{9}{x}−{29}{x}−{2}\)
pounds moves an object along a straight line when it is xx feet from the origin. Calculate the work done in moving the object from
\(\displaystyle{x}={1}{f}{t},\to,{P}{S}{K}{x}={19}{f}{t}.\)
(Round your answer to two decimal places.)
Integrals
asked 2021-03-09
Show by substitution that
\(\displaystyle{u}{\left({x},{t}\right)}={\cos{{\left(απ{x}\right)}}}{e}^{
Integrals
asked 2021-03-09
Compute
\(\displaystyle{\int_{{0}}^{{2}}}\frac{{1}}{{{x}-{1}}}{\left.{d}{x}\right.}\)
Integrals
asked 2021-03-09
Evaluate the integral
\(\displaystyle\int{e}^{{{3}{x}}} \cos{{2}}{x}{\left.{d}{x}\right.}\)
Integrals
asked 2021-03-07
A particle with velocity at any time t is given by
\(\displaystyle{v}{\left({t}\right)}={2}{e}^{{{2}{t}}}\)
moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4?
Integrals
asked 2021-03-06
Give the correct answer and solve the given equation
\([x-y \arctan(\frac{y}{x})]dx+x \arctan (\frac{y}{x})dy=0\)
Integrals
asked 2021-03-05
Give the correct answer and solve the given equation
\(dx + (\frac{x}{y} − \sin y)dy = 0\)
Integrals
asked 2021-02-24
\((x^{2}+2xy-4y^{2})dx-(x^{2}-8xy-4y^{2})dy=0\)
Integrals
asked 2021-02-21
Evaluate the integral:
\(\displaystyle\int\int\int_{{E}}{\left({x}{y}+{z}^{{2}}\right)}{d}{V}\)
,
where
\(\displaystyle{E}={\left\lbrace{\left({x},{y},{z}\right)}{\mid}{0}\le{x}\le{2},{0}\le{y}\le{1},{0}\le{z}{<}{3}\right\rbrace}\)
Integrals
asked 2021-02-18
\(\displaystyle{\int_{{{0}}}^{{{2}}}}{\frac{{{1}}}{{{\left({x}-{1}\right)}^{{{2}}}}}}{\left.{d}{x}\right.}\)
Integrals
asked 2021-02-12
Solve.
\(int (4ax^3+3bx^2+2cx)dx\)
Integrals
asked 2021-02-11
Solve
\(\displaystyle{\left.{d}{x}\right.}+{\left({x}{y}−{\sin{{y}}}\right)}{\left.{d}{y}\right.}={0}.\)
Integrals
asked 2021-02-11
Integration of
\(\displaystyle{\left({y}\cdot{\tan{{x}}}{y}\right)}\)
Integrals
asked 2021-02-09
Evaluate the integral
\(\displaystyle\int\frac{x}{{2}}{\left.{d}{x}\right.}\)
Integrals
asked 2021-02-08
\(\int_{8}^{21}f(x)dx-\int_{8}^{11}f(x)dx=\int_{a}^{b}f(x)dx\)
Integrals
asked 2021-02-06
Evaluate the triple integral
\(\displaystyle\int\int\int_{{E}}{3}{y}{d}{V}\)
,where
\(\displaystyle{E}={\left\lbrace{\left({x},{y},{z}\right)}{\mid}{0}\le{x}\le{2},{0}\le{y}\le\sqrt{{{4}-{x}^{{2}}}},{0}\le{z}\le{x}\right\rbrace}\)
Integrals
asked 2021-02-02
Evaluate the integral
\(\displaystyle\int{\frac{{{1}}}{{{1}+{\frac{{{x}}}{{{2}}}}^{{2}}}}}{\left.{d}{x}\right.}\)
Integrals
asked 2021-01-30
a) If
\(\displaystyle f{{\left({t}\right)}}={t}^{m}{\quad\text{and}\quad} g{{\left({t}\right)}}={t}^{n}\)
, where m and n are positive integers. show that
\(\displaystyle{f}\ast{g}={t}^{{{m}+{n}+{1}}}{\int_{{0}}^{{1}}}{u}^{m}{\left({1}-{u}\right)}^{n}{d}{u}\)
b) Use the convolution theorem to show that
\(\displaystyle{\int_{{0}}^{{1}}}{u}^{m}{\left({1}-{u}\right)}^{n}{d}{u}=\frac{{{m}!{n}!}}{{{\left({m}+{n}+{1}\right)}!}}\)
c) Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.
Integrals
asked 2021-01-28
Sketch the region bounded by the curves:
\(\displaystyle{y}={\ln{{x}}},{y}={0}{y}={\ln{{x}}},{y}={0}\)
and
\(\displaystyle{x}={e}{x}={e}\)
, then find, the area of this region, and find the volume of the solid generated by revolving this area about the line
\(\displaystyle{x}=−{2}?{x}=−{2}\)
?
Integrals
asked 2021-01-28
How trigonometric substitutions can helps in solving difficult integrals?
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