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hotwater
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Homework Statement
In Example 3 under Theorem 2.5 of Apostol's Calculus Volume 1, I don't understand how the final formula on the right is obtained.
Homework Equations
The identity cos 2x = 1 - 2 sin2 x implies sin2x = 1/2(1 - cos 2x) so, from Example 2, we obtain:
[tex]\int^a_0\,sin^2\,x\,dx = \frac{1}{2}\,\int^a_0(1 - cos\,2x)\,dx = \frac{a}{2} - \frac{1}{4}\,sin\,2a[/tex]
The Attempt at a Solution
I guess this uses (2.14), but I don't understand how:
(2.14): [tex]\int^{a}_{0}[/tex] sin x dx = 1 - cos a
Scribd has a copy of the book online, at http://www.scribd.com/doc/36116063/eBook-Tom-Apostol-Calculus#. My question is in regard to page 101, Example 3, near the bottom.
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