Finding area-FTC (is it right?)

[maks4]

1. The question is:
Find the area between the x-axis and the curve y=sinx on [0, PI]


2. And i think i did it right but i just want to make sure...
So an anti derivative of sinx is = -cosx
Evaluating comes to = -cos PI - (-cos 0) which comes out to 1+1=2

This is right, right?

And a second question as well

2. Find the area bounded by the curves y = x^2 and y = x^3 on the interval [0,1]
Ok here is the solution

What i don't understand here is, shouldn't (1/4 * x^4) be 0? Aren't you replacing the x with a 0 and doesn't the rest of it become 0? It just seems like only the 1 is evaluated on both of them and that's how it comes to 1/3 - 1/4...i don't understand how it came to that. (sorry if this is obvious but i can't see it)

 

[rock.freak667]

EDIT:
Looks correct.

 

[epkid08]

You forgot units squared, but yeah it looks right.

 

[maks4]

^^Thanks both of you. But what do you mean i forgot units squared?

 

[epkid08]

When stating an area, you're 'suppsed' to put units^2 after your constant.

 

[maks4]

Oh right, thanks!

 

[maks4]

Never mind about the second question i figured it out...:shy: