1. ## integration help

could someone explain how to solve problems like this one. an explanation would be more helpful than just an answer, thanks.

find the area between the curves y=cosx and the x axis bound by the lines x=0 and x=pi.

2. The integral of a function $f$ between two given points $a$ and $b$ gives you the "area" (apart from possibly a minus sign) between the graph of $f$ and the $x$ axis, bounded by the lines $x=a$ and $x=b$.

If the function is nonnegative, there is no minus sign, so the integral is exactly the area beneath the curve.

You want to compute the are beneath the graph of $\cos (x)$, bounded by the lines $x=0$ and $x=\pi$. First observe that, between $0$ and $\pi$, $\cos (x)\geq 0$. So all you have to do is integrate $\cos (x)$ with $x$ running from $0$ to $\pi$.

Edit: huge mistake from my part (was picturing $\sin (x)$ in my head instead of cosine). Obviously $\cos (x) \leq 0$ for $x\in [\frac{\pi}{2},\pi]$. I'm terribly sorry. The post below me says what needs to be said

3. Originally Posted by hyzlemon
could someone explain how to solve problems like this one. an explanation would be more helpful than just an answer, thanks.

find the area between the curves y=cosx and the x axis bound by the lines x=0 and x=pi.
$A = \int_0^{\frac{\pi}{2}} \cos{x} \, dx - \int_{\frac{\pi}{2}}^{\pi} \cos{x} \, dx$

now think about two things ...

1. why is the integral split at pi/2 ?

2. why is the second integral subtracted ?