anonymous
  • anonymous
Help with a few calc II problems for Trigometric Substitution? 10 | (100-x^2)^(1/2) dx 5 I have 6 others I am struggling with but I figured start one at a time. Thanks in advance.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{5}^{10} \sqrt{100-x^2}dx\] for a better version of the problem
BAdhi
  • BAdhi
Make the substitution of \(\sin \theta = \frac {x}{10} \) \(10\cos \theta d\theta = dx \) \[\int \limits_5^{10} 10\sqrt{1-(x/10)^2}dx = \int \limits_{0.5}^{1} 10\sqrt{1-\sin^2\theta}(10\cos \theta )d\theta\]
anonymous
  • anonymous
That much I got.

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BAdhi
  • BAdhi
tell us where is the problem then?
anonymous
  • anonymous
Well, I don't know where to go from here. I've been struggling with trigometric problems since day 1 and this is so far the most obnoxiously difficult. Also I converted b and a into radians.
BAdhi
  • BAdhi
\[100\cos \theta\sqrt{1-\sin^2\theta}= 100\cos^2 \theta\] The integral is finally sum up to- \[100\int\limits_{0.5}^{1}\cos^2\theta d\theta \] use double angle identity to replace \(\cos ^2\theta \) to \(\cos (2\theta)\)
anonymous
  • anonymous
Ok. so \[100\int\limits_{.5}^{1}\cos2 \theta d \theta. \] And from there? I'm really sorry, I have no idea what I'm doing with these. I just know the answer is supposed to be 25(2pi/3 - sqrt3/2)

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