I need help understanding Cosine sine area integral problem.?

Posted on 2015-12-07 07:09:00 in Math by JAYSEN

Find the area A of the region between the graph of f and the x-axis on the given interval

Let f(x) = cos(x) ? sin(x) for 0 ? x ? ?

I am thoroughly confused on how to solve this problem I can do area problems between the bounded region formed by one two and three functions. However, this single trig function (possibly two?) based problem I am struggling with.

My attempt:

First find a switching point by setting the entire function to zero.

cos(x) - sin(x) = 0
cos(x) = sin(x)

So then is this the same as saying x = y or y = x here?

I am confused what cos(x) = sin(x) even means. Like there is no value there just two blank functions I am unsure how to progress which drives me to foolishly integrate like this:

int_{0}^{?} (cos(x)-sin(x))dx

-sin(x)+cos(x) \bigg|_{0}^{?}

= -sin(?)+cos(?) - (sin(0)+cos(0))

= -1-1 = -2

Clearly this is wrong just by the fact that area is generating a negative number.

My may confusion is being able to find the switching point. Is there a way to interpret it algebraically instead of having to draw of the functions of sin(x) and cos(x) to see where that switching point happens?

---

Answer Comment

No Answers Posted Yet.