Eherre1989
can someone solve this for me without changing the limits of integration?
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Eherre1989
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\[\int\limits_{1}^{3}x \sqrt{1-(x-2)^2}dx\]
Eherre1989
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step by step please
Eherre1989
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it has to be a trig substitution i just get stuck when i have to integrate the sins
Mr.Math
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Write what you have so far.
Eherre1989
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\[\int\limits_{}^{}(\sin \theta-\sin^3\theta-2\sin^2\theta+2)d \theta\]
Eherre1989
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i need that integrated i cant seem to figure out the middle two
Eherre1989
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i feel as if i should do by parts
Mr.Math
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Break it down into four integrals. I'm sure you know how to integrate \(\sin\theta\) and \(2\).
Mr.Math
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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 \(-\cos^2\theta\sin\theta\).
Eherre1989
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i dont remember any trig identities
Mr.Math
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\(\sin^2\theta=\frac{1-\cos(2\theta)}{2}\).
Mr.Math
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Sorry it should be \(-2\sin^2\theta=\cos(2\theta)-1\).
Eherre1989
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oh ok thanks
Mr.Math
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You're welcome.