Riemann integral

**TexasGirl** · September 3rd 2006, 03:32 PM

Compute the Riemann integral of the absolute value of sinx from 0 to 2(pi)

**ThePerfectHacker** · September 3rd 2006, 03:36 PM

Originally Posted by TexasGirl

Compute the Riemann integral of the absolute value of sinx from 0 to 2(pi)

We note that,
$f=|\sin x|$ is countinous thus it exists.
If $0\leq x\leq \pi$
Then, $f=\sin x$ by the definition of absolute value.
If $\pi \leq x\leq 2\pi$
Then, $f=-\sin x$ by the definition of absolute value.
Thus, by the subdivision rule,
$\int_0^{2\pi}|\sin x|dx=\int_0^{\pi}\sin xdx+\int_{\pi}^{2\pi} -\sin xdx$
I assume you can solve it from heir.

**TexasGirl** · September 3rd 2006, 03:59 PM

yep...thanks

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