# Simple calculus integration help

## Homework Statement

Integrate with an upper bound of 2 and a lower bound of -3
(4-y^2) - (y-2) dy

## The Attempt at a Solution

The books answer is 125/6 I have tried twice and got 29.5/3 and 6 : /

This will be my second time taking calculus 2 and I always have a hard time getting back into the zone of differentiation and integration.

I first simplified the equation into upper bound of 2 lower bound of -3 6-y^2-y dy

Then I integrated it piece by piece.
6 turns into 6y,
-y^2 turns into -y^3 /3
-y turns into -y^2/2

Then I plug in 2 for all the y's to give me A
Then I plug in -3 for all the y's to give me B
Then I do A-B (Upper bound plugged in minus lower bound plugged in) and I get 29.5/3

What am I doing wrong?

Thanks
-Dave

Mark44
Mentor
Lavid2002 said:
I first simplified the equation ...
This is an integral, not an equation.

You are probably making a sign error somewhere, since your antiderivative is correct.
$$\left. 6y - \frac{y^2}{2} - \frac{y^3}{3}\right|_{-3}^2$$
= (6(2) - 4/2 - 8/3) - (-18 - 9/2 + 27/3 )

If you are careful in evaluating this, you should get 125/6.

eumyang
Homework Helper
Then I plug in 2 for all the y's to give me A
Then I plug in -3 for all the y's to give me B
Then I do A-B (Upper bound plugged in minus lower bound plugged in) and I get 29.5/3

What am I doing wrong?

Thanks
-Dave
You're probably making some algebraic errors. When I plug in 2 I get 22/3, and when I plug in -3 I get -27/2.
22/3 - (-27/2) = 125/6

EDIT: Oops, beaten to it. ;)

I got it now : /

This is what messes me up in this class. Not the calc II, the simple calc I and the algebra!
Very frustrating.

First homework assignment down.

Thanks bud

Mark44
Mentor
This is what messes me up in this class. Not the calc II, the simple calc I and the algebra!
Very frustrating.
This is not unique to you. Unlike many other subjects, math builds on knowledge and skills from previous classes. If you find that you are having difficulties with techniques that were presented in earlier classes, set aside some time to spend reviewing those techniques and working a few problems. A small investment of time now will help you out a lot later on.