Evaluate the line integral along the path C given by $x=2t,\text{}y=10t,$ where $0\le t\le 1\int cxydx+ydy$

Barbara Schroder
2021-11-15
Answered

Evaluate the line integral along the path C given by $x=2t,\text{}y=10t,$ where $0\le t\le 1\int cxydx+ydy$

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Momp1989

Answered 2021-11-16
Author has **21** answers

Given that

Therefore,

Substitute the value to get

Given that

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Evaluate the line integral, where C is the given curve

C xy ds

C:$x={t}^{2},y=2t,0\le t\le 5$

C xy ds

C:

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Evaluate the following integrals.

$\int \frac{x+4}{{x}^{2}+8x+25}dx$

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A ball is dropped from the top of a tall building. If air resistance is taken into account, recall that the downward velocity v of the ball is modeled by the differential equation:

$dv/dt=g-pv$

where g = 9.8 $m/se{c}^{2}$ is the acceleration due to gravity, and p = 0.1 is the drag coefficient. Assuming the initial velocity of the ball is zero, use Euler’s method with a step size of h = .25 sec to estimate the velocity of the ball after one second. Keep track of three decimal places during the calculation.

I just started learning the Euler's method. Can someone help me with this problem. I know that:

$dv/dt=f(v,t)=g-pv$

I plug the numbers given into the equation: $dv/dt=9.8-.25v$

change of x = step size (h) = .25

I think $(v(0),t(0))=(0,0)$??

$dv/dt=g-pv$

where g = 9.8 $m/se{c}^{2}$ is the acceleration due to gravity, and p = 0.1 is the drag coefficient. Assuming the initial velocity of the ball is zero, use Euler’s method with a step size of h = .25 sec to estimate the velocity of the ball after one second. Keep track of three decimal places during the calculation.

I just started learning the Euler's method. Can someone help me with this problem. I know that:

$dv/dt=f(v,t)=g-pv$

I plug the numbers given into the equation: $dv/dt=9.8-.25v$

change of x = step size (h) = .25

I think $(v(0),t(0))=(0,0)$??

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Integrate $\frac{8}{7}{x}^{3}\mathrm{tan}({x}^{4}+4)\mathrm{sec}({x}^{4}+4)$ with respect to x.

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calculate the complex integral limit

$\underset{T\to \mathrm{\infty}}{lim}\frac{1}{2\pi i}{\int}_{c-iT}^{c+iT}\frac{{x}^{s}}{{s}^{k+1}}ds$

where$c>0$ and $k\ge 1$ is an integer.

where