anonymous
  • anonymous
how do you find the integral of the following: integral sqrt 9-h^2 limits 0 to 3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Are you learning about trig substitutions or polar coordinates?
anonymous
  • anonymous
hey i have a test and i am review for it, its trig sunsitution
anonymous
  • anonymous
substitute = 3 sin x

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anonymous
  • anonymous
Since in the limit of integral,0a=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
  • anonymous
Okay, 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 \[\cos \theta=\sqrt {9-h^2}/3\] 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 back-substitute.
anonymous
  • anonymous
you can also draw a circle with radius 9 and conclude that the area is just one-fourth of the circle...
anonymous
  • anonymous
radius 3, silly me
anonymous
  • anonymous
okay thank you for the explanation but this question but this question is related to another problem u think u can help me
anonymous
  • anonymous
ok
anonymous
  • anonymous
can 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
  • anonymous
What area do you need? The area between the two chords?
anonymous
  • anonymous
no thats the strip and u have to use the strip to find the area of the entire circle
anonymous
  • anonymous
you would have to first write riemann sum then the definite integral

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