Difference between revisions of "User:Annoyingpi"
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+ | Find the integral for the arc length of <math>x^2 + y^2 = 4</math> going clockwise from <math>(-3^{0.5}, 1)</math> to <math>(3^{0.5}, 1)</math>. | ||
+ | |||
+ | The function is <math>y = \sqrt{4-x^2}</math>. <math>x</math> is ranging from <math>-\sqrt{3}</math> to <math>\sqrt3</math>. | ||
+ | |||
+ | <cmath> | ||
+ | \frac{dy}{dx} = -x \frac1{\sqrt{4-x^2}}. | ||
+ | </cmath> | ||
+ | |||
+ | Therefore the integral is | ||
+ | <cmath> | ||
+ | \boxed{\int_{-\sqrt3}^{\sqrt3} \sqrt{1+ \frac{x^2}{4-x^2}} \, dx}. | ||
+ | </cmath> | ||
+ | |||
+ | '''IGNORE EVERYTHING BELOW:''' | ||
+ | |||
<asy> | <asy> | ||
draw((0,0)--(0,2)--(2,2)--(2,0)--cycle); | draw((0,0)--(0,2)--(2,2)--(2,0)--cycle); |
Revision as of 17:41, 28 November 2008
Find the integral for the arc length of going clockwise from
to
.
The function is .
is ranging from
to
.
Therefore the integral is
IGNORE EVERYTHING BELOW: