anonymous
  • anonymous
can someone solve this for me without changing the limits of integration?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{1}^{3}x \sqrt{1-(x-2)^2}dx\]
anonymous
  • anonymous
step by step please
anonymous
  • anonymous
it has to be a trig substitution i just get stuck when i have to integrate the sins

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Mr.Math
  • Mr.Math
Write what you have so far.
anonymous
  • anonymous
\[\int\limits_{}^{}(\sin \theta-\sin^3\theta-2\sin^2\theta+2)d \theta\]
anonymous
  • anonymous
i need that integrated i cant seem to figure out the middle two
anonymous
  • anonymous
i feel as if i should do by parts
Mr.Math
  • Mr.Math
Break it down into four integrals. I'm sure you know how to integrate \(\sin\theta\) and \(2\).
Mr.Math
  • Mr.Math
For \(\sin^3\theta\), write \(\sin^3\theta=\sin\theta-\cos^2\theta\sin\theta\), and then the integral of \(\sin\theta\) is easy. Substitute \(u=\cos\theta\) for the integration of \(-\cos^2\theta\sin\theta\).
anonymous
  • anonymous
i dont remember any trig identities
Mr.Math
  • Mr.Math
\(\sin^2\theta=\frac{1-\cos(2\theta)}{2}\).
Mr.Math
  • Mr.Math
Sorry it should be \(-2\sin^2\theta=\cos(2\theta)-1\).
anonymous
  • anonymous
oh ok thanks
Mr.Math
  • Mr.Math
You're welcome.

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