A couple of integration problems

1. Apr 1, 2012

Cacophony

1. The problem statement, all variables and given/known data
a) S(4 is higher limit, 0 is lower limit) (x^4 - x^2 + 1)dx

b) S(pi is higher limit, -pi is lower limit) (cosx + sinx)dx

2. Relevant equations

The S is the integration sign

3. The attempt at a solution

a) = ((x^5)/5)-((x^3)/3)+x I(4 high, 0 low)

= (((4^5)/5)-((4^3)/3)+4)-(0)

Is this the final solution or is there another step i don't know about?

b) = (sinx + -cosx) dx I(pi high, -pi low)
= (sin(pi)-cos(pi))-(sin(-pi)-cos(-pi))

Is this the final solution?

2. Apr 1, 2012

LCKurtz

While your answers are technically correct, you should simplify them both. Put in the values of $\cos \pi$ and $\sin \pi$.

3. Apr 1, 2012

Cacophony

so basically:

(0-1)-(0-1)?

4. Apr 1, 2012

5. Apr 1, 2012

0 right

6. Apr 1, 2012

Cacophony

do I simplify the first one aswell? Cause someone said I didn't have to.

7. Apr 1, 2012

LCKurtz

0 is the correct answer, but I'm not sure you didn't make a couple of cancelling arithmetic mistakes along the way. In post #3 it appears you made the following step:

(sin(pi)-cos(pi))-(sin(-pi)-cos(-pi))
= (0-1)-(0-1)

The arithmetic in that step has two errors. With regard to your first one, I wouldn't consider it simplified until it is a single fraction reduced to lowest terms.

8. Apr 1, 2012

Cacophony

I'm not following. What do you mean reduced to lowest terms?

9. Apr 1, 2012

LCKurtz

(((4^5)/5)-((4^3)/3)+4)-(0)

I mean combine the three terms into a single fraction; get rid of all those parentheses.

A fraction is reduced to lowest terms when the numerator and denominator have no common factors. For example, you wouldn't leave an answer as $\frac{42}{30}$ when it could be reduced to $\frac{7}{5}$.
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