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anonymous
 5 years ago
how do you find the integral of the following:
integral sqrt 9h^2 limits 0 to 3
anonymous
 5 years ago
how do you find the integral of the following: integral sqrt 9h^2 limits 0 to 3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you learning about trig substitutions or polar coordinates?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey i have a test and i am review for it, its trig sunsitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since in the limit of integral,0<h<3, so u can substitute h=3sin(a) since sin is btw 0 and 1, then (9h^2) becomes 9cos^(a) take sqrt=3cos(a) also dh=d(3sin(a))=3cos(a)da thus and change limits h=0=3sin(a)=>a=0 h=3=3sin(a)=>a=pi/2 thus integral becomes limit 0 to 1 9cos^2(a)da put cos^2(a)=(2cos^(2a)1)/2 then integrate

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, since we have sqrt(a^2  u^2) form, we have to use a sin t substitution. Let u = asint \[h = 3\sin \theta\] You should find that sine of theta is equal to h / 3. Use SOHCAHTOA to draw a right triangle. One leg should be h and the hypotenuse should be 3. Find the other leg using the pythagorean theorem to get sqrt(9  h^2). Take the cosine of the angle \[\cos \theta=\sqrt {9h^2}/3\] Multiply by 3 on both sides to get cosine(theta)/3 to use as a substitution. Substitute that for sqrt(9  h^2) in the integral. Now go back to the h = 3sin(theta) equation and take the derivative to get dh = 3cos(theta). Substitute 3cos(theta) for dh to get the integral: \[\int\limits_{\theta(0)}^{\theta(3)}\cos \theta /3*3\cos \theta d \theta\] \[\int\limits_{\theta (0)}^{\theta (3)}\cos ^2 \theta d \theta\] You'll then have to integrate that and backsubstitute.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can also draw a circle with radius 9 and conclude that the area is just onefourth of the circle...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay thank you for the explanation but this question but this question is related to another problem u think u can help me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can u please click on the link to see the picture i have to find the area by writing the definite integral and evaluate it http://www.twiddla.com/504415

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What area do you need? The area between the two chords?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no thats the strip and u have to use the strip to find the area of the entire circle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you would have to first write riemann sum then the definite integral
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