### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# 47 Class Note for MATH 230 at PSU

### View Full Document

## 19

## 0

## Popular in Course

## Popular in Department

This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 19 views.

## Similar to Course at Penn State

## Popular in Subject

## Reviews for 47 Class Note for MATH 230 at PSU

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

Sample Test 4 1 True or False Clearly indicate your Choice a T F 02lsfxy dx dy1502fxy dx dy b T F Let a the area of the region R in the zy plane lf ay k for all z and y in R7 then ay dA ka R 7r2 1 C T F Vol ofsphere x2y2221is given byV8 17r2rdrd6 0 0 2 27r 35in9 2 35in9 dT F p2s1n dpd6d 27rOO pzsina dpda 2 5 2 dsdy 0 3 a2 b 5 C 4 d e 10 f Does not Exist 3 Aljxlizzdydz a b i C i d 1 e 2 f 2X N H 4 The following integral de nes the volume of the region inside the sphere 2 y2 22 a2 above the xy plane over the region x2 y2 S 1 1 11712 dazixziyz dy dx 1 7W When this is converted to polar coordinates7 the resulting double integral has the form 27r 1 27r 1 27r 1 a r2 dr d0 b r a2 7 r2 d0 dr 0 7 dr d0 0 0 0 0 0 0 d 027r fol W d7 d9 e 027 017 Va 7 r2 dr d6 2 m2 5 The iterated integral ay dy dx is equivalent to 0 0 a 040 fzy dx dy b A4fzy dx dy C AZjg sy dx dy d O4fltwgtdx dy e 02fltwgtdx dy 10 11 12 13 14 15 16 17 18 6 6 Evaluate the following iterated integral Exact answers only No numerical approximations ey2 dy dx 0 m Express the following as a single iterated integral Do not evaluate it 2 m 4 47m dy dp dy dx 0 0 2 0 Find the COM of the triangle whose vertices are 007 017 20 and whose density is given by Wt 11 ky Set up but do not evaluate a double integral that gives the area of the surface on the graph of ay zey over the region R consisting of all z and y such that 0 S x S 4 and 0 S y S 10 Set up but do not evaluate a triple integral for the mass of the solid region Q bounded by the graphs of the equations below Assume that density is proportional to the distance from the origin Q 227y7 207 1107 3 z0 Suppose Q is the region in space above the xy plane inside the sphere 2 y2 22 16 Consider the integral 952 2 dV Qlt y a Set up but do not evaluate an iterated triple integral in cylindrical coordinates that could be used to evaluate this integral b Set up but do not evaluate an iterated triple integral in any co ordinates that nds the COM of Q Find the volume of the solid below 2 x2 y2 over the region R x2 y2 S 1 Use a double integral in polar coordinates to nd the volume ofthe solid of x7 y e wH over the region 2 y2 S 1 Show your work Exact answers only NO NUMERICAL APPROXIMATIONS Find area of parallelogram with vertices 004163 and 22 by attempting a change of variables via z 4u 7 1 and y 7 1Hiht The sides are parallel to y z and z 4y Using a change of variable7 compute x y2 sinx 7 y dA where R is the square with vertices R W70 lt37quot 713977139 g Hint use u xyw x7y the square have sidesz7y 7T z7y 07zy7rxy27r Bonus 1 Page 1041 Section Project Find the volume of the Wrinkled Sphere and the Bumpy Sphere Bonus 2 Page 1041 Question 46 Bonus 3 Find the volume of the four dimensinal ellipsoid 2 y2 222 1 2w2 1

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.