×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

Create a StudySoup account

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

or

By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

14

0

10

Class Note for MATH 250A with Professor Lega at UA

Marketplace > University of Arizona > Class Note for MATH 250A with Professor Lega at UA

No professor available

Almost Ready

These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

About this Document

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
10
WORDS
KARMA
25 ?

Popular in Department

This 10 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 14 views.

×

Reviews for Class Note for MATH 250A with Professor Lega at UA

×

×

What is Karma?

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
Calculus and Differential Equations ll MATH 250 B Area volume arc length density and center of mass Areas and volumes 0 Example 1 We want to calculate the area of the region between the curves of equation y X and y for X 6 01 0 Draw a picture and calculate the area using 0 Horizontal slices 9 Vertical slices 9 Select your answer 0 12 a 13 9 16 9 18 9 Example 2 Find the volume of a prism with sides of length 27 3 and 4 centimeters 0 Recall that if you have to choose how to slice an object try to make your task as simple as possible Areas and volumes continued Which of the graphs below represent the area as a function of X of the region between the two curves shown in the plot on the left a Area volume arc length density and center of mass Calculus and Differential Equations l Areas and volumes continued Which of the graphs below represent the area as a function of X of the region between the two curves shown in the plot on the left M in 7r2 7r 37r2 2n 1r2 7r 3M2 2n wk IQ 2 W 312 27 7r2 739 37r2 2 Area volume arc length density and center of mass Calculus and Differential Equations ll Volumes 0 Example 1 Find the volume of the object obtained by rotating the region bounded by y X 1 and y 0 about the axis of equation X 1 0 Example 2 Find the volume of the object obtained by rotating the region R bounded by y expX X 0 X 1 and the X axis about the line of equation y 7 0 Example 3 Find the volume of the object whose base is the region R defined above and whose cross sections perpendicular to the X axis are squares a Which formula represents the volume of the solid obtained by rotating the region between the 2 curves about the y axis o 0q27rxfxegx dx 9 Oqfxegx dx 9 0q7rfxegx2 dx 0 Oq7rfx2e7rgx2 dx 9 quxfxigx dX Area volume arr length density and Center of malt Calculus and Differential Equations Arc length 9 To compute the length of a curve think of a particle moving along the curve and integrate its velocity as a function of time 9 Of course the above assumes that the particle always moves in the same direction along the curve ie that its speed does not change sign 0 Then if the curve is given as the graph of a function say y fx for X E 3 b then its length I is Iab l l f x2 dx 0 Alternatively if the curve is given in parametric form ie if we know Xt and yt for t 6 17 t2 then x t2 y t2 dr Arc length continued 0 Example 1 Consider a curve described by X t and y ft Do the two formulas given above match 9 Example 2 Find the arc length of the curve of equation y X32 for X 6 02 and indicate which of the possible answers below is correct WY11gt WV11gt Was11gt Arc length continued Which of the graphs below represents the arc length of the curve shown on the left a 1 b y 10 e 16 12 12 y 1 2 8 8 10 4 4 8 41iiiu T 41iiiu I 1 2 3 4 J 1 2 3 4 5 6 c y d y 16 e 16 e 4 12 12 2 8 3 I 1 2 3 4 3 4 4 41iiiu r 41iiiu I 1 2 3 4 5 1 2 3 4 a Area volume arc length density and center of mass Calculus and Differential Equations l Density and center of mass 0 Here we only consider objects that are one dimensional As a consequence their density is given in units of mass per unit length eg gcm 9 Example Find the mass of a rod of length 10 cm and of density 6X eXp7X grams per centimeter for X 6 010 0 The center of mass of a collection of N particles of mass m at positions X is the point with coordinate o By analogy the center of mass of a rod of density 6X starting at X a and ending at X b has coordinate fabX6X dX fab 6X dX 39 7

×

×

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

Bentley McCaw University of Florida

"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!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over \$500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

Forbes

"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."

Become an Elite Notetaker and start selling your notes online!
×

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.