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**banshee.beat** Hey. So, I'm having trouble figuring out how to solve this integral. And I would really appreciate it if someone could help me.

$\displaystyle \int_0^{\frac{3\pi}{2}}|sinx|dx$

Okay, so I know I need to split the integral because it is an absolute value. But I'm unsure of what values I need to use to do that. Can I just pick any value I want?

Mr F says: Draw the graph first by reflecting in the x-axis the parts of the graph of y = sin x that are below the x-axis. Then it should be quite obvious what the intervals need to be.

Also, I've been working on this problem, can someone tell me if I am approaching it correctly?

$\displaystyle g(x)=\int_{tanx}^{x^{2}}\frac{1}{\sqrt{2+t^4}}dt$

Here is what I have thus far:

$\displaystyle \int_{tanx}^{0}\frac{1}{\sqrt{2+t^4}}dt+\int_{0}^{ x^{2}}\frac{1}{\sqrt{2+t^4}}dt$

$\displaystyle -\int_{0}^{tanx}\frac{1}{\sqrt{2+t^4}}dt+\int_{0}^{ x^2}\frac{1}{\sqrt{2+t^4}}dt$

$\displaystyle g'(x)=\frac{-1}{\sqrt{2+tan{\color{red}^4} x}}\, \frac{d}{dx}(tanx)+\frac{1}{\sqrt{2+x^{\color{red} 8}}}\, \frac{d}{dx}(x^2)$

..and that's all I have so far, but I'm not really sure what I need to do. Or if I'm even doing it correctly. Mr F says: It's almost OK (see the mistakes I corrected in red). Obviously the next step is to calculate the derivatives ....

Thanks!!!!