SOLUTION: Use the reverse chain rule to find integral of cosec^3xcotx in terms of dx, bounds pi/6 to pi/4
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Question 1121444: Use the reverse chain rule to find integral of cosec^3xcotx in terms of dx, bounds pi/6 to pi/4
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\cot(x)dx)
Let )
, then \frac{d}{dx}\csc(x)\ =\ -3\cot(x)\csc(x)\csc^2(x)\ =\ -3\cot(x)\csc^3(x))
. Therefore \csc^3(x)}du)
. Substituting:
\cot(x)dx\ =\ -\frac{1}{3}\int\,du\ =\ -\frac{1}{3}u\ +\ C)
Reversing the substitution:
}{3})
The rest is just arithmetic. Hint: 
is the reciprocal of 
and you should know the values for )
and )
by now.
John
My calculator said it, I believe it, that settles it
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