anonymous
  • anonymous
Steps for integrating
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{\pi/4}^{\pi/2} (2\sin \theta)^2 d \theta\]
anonymous
  • anonymous
i take it this is the same as \[4\int \sin^2(x)dx\] right?
anonymous
  • anonymous
Yes

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dumbcow
  • dumbcow
integration by parts twice
anonymous
  • anonymous
gimmick is to write \[\sin^2(x)=1-\cos^2(x)=\frac{1}{2}-\frac{1}{2}\cos(2x)\] one of those "double angle formula's backwards"
anonymous
  • anonymous
best trick is actually to look in the back of the textbook for the "reduction formulas" but if you recall all those annoying trig identities, this is the "lowering powers" formula
anonymous
  • anonymous
Ah, thanks. I get it.
anonymous
  • anonymous
yw
amistre64
  • amistre64
sin reduction:\[\int sin^ndx=-\frac{1}{n}sin^{n-1}cos+\frac{n-1}{n}\int sin^{n-2}dx\]
anonymous
  • anonymous
yeah that one that i can't remember. the entire content of most calc 2 courses is contained on the back two pages of the text
anonymous
  • anonymous
I've never seen that formula but wouldn't that give me another answer?
amistre64
  • amistre64
the answer might "look" different, but since trig has identities that are equal it will have the same value in the end
amistre64
  • amistre64
using integration by parts ends up with that formula for reduction

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