New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

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

Sign up with Facebook


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

Already have a StudySoup account? Login here

Class Note for MATH 1314 with Professor Flagg at UH 2


Class Note for MATH 1314 with Professor Flagg at UH 2

Marketplace > University of Houston > Class Note for MATH 1314 with Professor Flagg at UH 2

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
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

View Preview

About this Document

No professor available
Class Notes
25 ?




Popular in Course

Popular in Department

This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 22 views.

Similar to Course at UH


Reviews for Class Note for MATH 1314 with Professor Flagg at UH 2


Report this Material


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
Page 1 of6 Math 1314 Lesson 18 Area and the De nite Integral We are now ready to tackle the second basic question of calculus 7 the area question We can easily compute the area under the graph of a function so long as the shape of the region conforms to something for which we have a formula for geometry Example 1 Suppose f x 5 Find the area under the graph of f x from x 0 to x 4 Approximating Area Under a Curve Now suppose the area under the curve is not something whose area can be easily computed We ll need to develop a method for finding such an area Example 2 Here we ll draw some rectangles to approximate the area under the curve We can find the area of each rectangle then add up the areas to approximate the area under the curve Math 1314 Lesson 18 Page 1 of6 Page 2 of 6 Example 3 Next We ll increase the number of rectangles Example 4 And We ll increase the number of rectangles again 1W Math 1314 Lesson 18 Page 2 of6 Page 3 of6 What you should see is that as the number of rectangles increases the area we compute using this method becomes more accurate The Area Under the Graph of a Function Let f be a nonnegative continuous function on 61 b Then the area of the region under the graph of f is given by A1iIgfxlfxZfxnAx b a n where x1 x2 x are arbitrary points in the interval a b of equal width Ax The sums of areas of rectangles are called Riemann sums and are named after a German mathematician Example 4 Use left endpoints and 4 subdivisions of the interval to approximate the area under f x 2x2 l on the interval 0 2 Math 1314 Lesson 18 Page 3 of6 Page 4 of6 Example 5 Use right endpoints and 4 subdivisions of the interval to approximate the area under f x 2x2 1 on the interval0 2 Example 6 Use midpoints and 4 subdivisions of the interval to approximate the area under f x 2x2 1 on the interval 0 2 Math 1314 Lesson 18 Page 4 of6 Page 5 of6 Example 7 Suppose f x 1 3x Approximate the area under the graph of f on the interval 0 12 using 6 subdivisions and left endpoints The De nite Integral Letfbe de ned on a b If limfx1 fx2 fxn Axexists for all choices of b a representative points in the n subintervals of a b of equal width Ax then this n limit is called the de nite integral of f from a to b The de nite integral is noted by r7 fxdxlimfx1 fx2 fxn Ax The number a is called the lower limit of integration and the number b is called the upper limit of integration A function is said to be integrable on a b if it is continuous on the interval a b Math 1314 Lesson 18 Page 5 of6 Page 6 of6 The de nite integral ofa nonnegative function The de nite integral of a general function From this section you should be able to Explain the procedure used to approximate area under a curve Use Riemann sums to approximate the area under a curve using right endpoints left endpoints or midpoints Explain what we mean by de nite integral of a nonnegative function or a general function Math 1314 Lesson 18 Page 6 of6


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."


"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


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


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:

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

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.