Question

Definite integral:
Between y=cos(t) and y=Sin(t)
Window of 0 < t < Pi
How do I know which one to subtract from the other?

Answer 1

If you graph them, the function that is on bottom is subtracted from the other. So, in this case the cosine function is the top function over this interval.

Answer 2

I can't tell which one is on bottom
Bottom in relation to what? or which axis?

Answer 3

Bottom in relation to a graph. Even if you do if opposite you will just get a negative number. So, that negative number will clue you that you picked the wrong function to subtract.

If you are integrating with respect to the x-axis it is the larger function over the smaller. If you are integrating with respect to the y-axis is is again large function (but it is to the right, not on top in this case)

Answer 4

the answer is 2.828 in the book but I tried integral of sin and cos subtract eachother and I get -2 or 2.
Im using Math then 9 key on my Ti-84

Answer 5

My mistake, the upper and lower bounds change. The graph of sine and cosine switch top/bottom in that interval when sin(x)=cos(x) so when x = pi/4.
You have integrate two different times. The first is cos(x)-sin(x) from 0 to pi/4 the second is sin(x)-cos(x) from pi/4 to pi

Answer 6

So I use the intercection point? How do I know to use pi/4, can you tell me why the bounds change? I still don't get it.

Answer 7

Alright, so i found pi/4 by setting cos(x)=sin(x) (yes, the intersection point). Sometimes two graphs can intersect and the one that is on top will not change, but not in this case. The subtraction of the graphs change because sin is now on top. It is really helpful to do a rough sketch of graphs when doing this. Just a few key points helps.

Answer 8

OK I think up until this point I was doing things like 5ln(2x) and y=3
So that I only had to find the area under one function to the other, but not an intercection point