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Here's what students ask on Applications of integrals
Applications of integrals
asked 2021-03-09
Evaluate the following integral.
\(\displaystyle\int{2}{x}{\left({1}-{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-03-09
Evaluate the following definite integral.
\(\displaystyle{\int_{{{0}}}^{{\pi}}}{x}{\sin{{x}}}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-03-07
Use areas to evaluate the integral.
\(\displaystyle{\int_{{{a}}}^{{{11}{b}}}}{2}{s}\ {d}{s},{0}{<}{a}{<}{b}\)
Applications of integrals
asked 2021-03-07
Evaluate the integral.
\(\displaystyle\int\frac{{{3}-{x}}}{{\sqrt{{x}}}}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-03-07
Consider the integral as attached, To determine the convergence or divergence of the integral, how many improper integrals must be analyzed? What must be true of each of these integrals for the given integral to converge?
\(\displaystyle{\int_{{0}}^{{3}}}\frac{{10}}{{{x}^{{2}}-{2}{x}}}{\left.{d}{x}\right.}\)
.
Applications of integrals
asked 2021-03-05
Evaluate the following definite integral.
\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{x}{\cos{{2}}}{x}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-03-04
Evaluate the integral.
\(\displaystyle\int{8}{\sin{{\left({4}{t}\right)}}}{\sin{{\left(\frac{{t}}{{2}}\right)}}}{\left.{d}{t}\right.}\)
Applications of integrals
asked 2021-02-27
Applications of double integrals:
A lamina occupies the part of the disk
\(\displaystyle{x}^{{2}}+{y}^{{2}}\le{64}\)
in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis.
Applications of integrals
asked 2021-02-26
given
\(\displaystyle{y}=\frac{{1}}{{x}}\)
is a solution
\(\displaystyle{2}{x}^{{2}}{d}{2}\frac{{y}}{{\left.{d}{x}\right.}}+{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{3}{y}={0},{x}{>}{0}\)
a) Find a linearly independent solution by reduction the order approach
b) Show that 2 solutions are linearly independent
c) Write a general solution
Applications of integrals
asked 2021-02-25
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
\(\displaystyle{y}={5}\frac{{\left({16}−{x}^{{2}}\right)}^{{1}}}{{2}}\)
, y = 0, x = 2, x = 3, about the x-axis
Applications of integrals
asked 2021-02-25
Evaluate the integral using the indicated substitution.
\(\displaystyle\int{\cot{{x}}}{\cos{{e}}}{c}^{{{2}}}{x}{\left.{d}{x}\right.},\ {u}={\cot{{x}}}\)
Applications of integrals
asked 2021-02-24
Solve the integral.
\(\displaystyle\int{x}{\ln{{x}}}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-02-21
Evaluate the integral using the indicated substitution.
\(\displaystyle\int{{\cos}^{{{2}}}{x}}{\sin{{x}}}{\left.{d}{x}\right.},\ {u}={\cos{{x}}}\)
Applications of integrals
asked 2021-02-21
Suppose
\(\displaystyle{\int_{{5}}^{{6}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}={6}{\quad\text{and}\quad}{\int_{{5}}^{{6}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}={2}\)
.
Evaluate
\(\displaystyle{\int_{{5}}^{{6}}}{\left({4}{f{{\left({x}\right)}}}-{2}{g{{\left({x}\right)}}}\right)}{\left.{d}{x}\right.}\)
.
Remember to include a "+ C"if appropriate.
Applications of integrals
asked 2021-02-20
Right, or wrong? Say which for each formula and give a brief reason for each answer.
\(\displaystyle\int{\left({2}{x}+{1}\right)}{2}{\left.{d}{x}\right.}={\left({2}{x}+{1}\right)}\frac{{3}}{{3}}+{C}\)
Applications of integrals
asked 2021-02-19
Trigonometric integral Evaluate the following integrals.
\(\displaystyle\int{{\sin}^{{2}}{0}}{{\cos}^{{5}}{0}}{d}{0}\)
Applications of integrals
asked 2021-02-19
Evaluate the following definite integrals:
\(\displaystyle{\int_{{0}}^{{1}}}{\left({x}{e}^{{-{x}^{{2}}+{2}}}\right)}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-02-18
Evaluate the following definite integrals
\(\displaystyle{\int_{{{0}}}^{{{1}}}}{x}{e}^{{{\left(-{x}^{{{2}}}+{2}\right)}}}{\left.{d}{x}\right.}\)
Applications of integrals
asked 2021-02-16
Evaluate the following integrals.
\(\displaystyle\int{{\sin}^{{{2}}}{0}}{{\cos}^{{{5}}}{0}}{d}{0}\)
Applications of integrals
asked 2021-02-16
Evaluate the following integrals.
\(\displaystyle{\int_{{-{{2}}}}^{{-{{1}}}}}\sqrt{{-{4}{x}-{x}^{{2}}}}{\left.{d}{x}\right.}\)
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