Download presentation

Presentation is loading. Please wait.

Published byRussell Ely Modified over 3 years ago

1
Review Problem – Riemann Sums Use a right Riemann Sum with 3 subintervals to approximate the definite integral:

2
Applications of the Definite Integral Mr. Reed AP Calculus AB

3
Finding Areas Bounded by Curves To get the physical area bounded by 2 curves: 1.Graph curves & find intersection points – limits of integration 2.Identify “top” curve & “bottom” curve OR “right-most” curve & “left-most” curve 3.Draw a representative rectangle 4.Set up integrand: Top – Bottom Right – Left

4
Finding Intersection Points Set equations equal to each other and solve algebraically Graph both equations and numerically find intersection points

5
Example #1 Find the area of the region between y = sec 2 x and y = sinx from x = 0 to x = pi/4.

6
Example #2 Find the area that is bounded between the horizontal line y = 1 and the curve y = cos 2 x between x = 0 and x = pi.

7
Example #3 From Text – p.240 - #16

8
Example #4 Find the area of the region R in the first quadrant that is bounded above by y = sqrt(x) and below by the x-axis and the line y = x – 2.

9
Summarize the process

10
AP MC Area Problem #12 from College Board Course Description

11
Homework P.236-240: Q1-Q10, 13-25(odd)

12
Authentic Applications for the Definite Integral Example #2 – p.237

13
Definite Integral Applied to Volume 2 general types of problems: 1.Volume by revolution 2.Volumes by base

14
Volume by Revolution – Disk Method The region under the graph of y = sqrt(x) from x = 0 to x = 2 is rotated about the x-axis to form a solid. Find its volume.

15
Volume by Revolution – Disk Method

16
Homework #1 – Disk Method about x and y axis P.246-247: Q1-Q10,1,3,5

17
Volume by Revolution – About another axis The region bounded by y = 2 – x^2 and y = 1 is rotated about the line y = 1. Find the volume of the resulting solid.

18
Volume by Revolution – Washer Method Find the volume of the solid formed by revolving the region bounded by the graphs of f(x) = sqrt(x) and g(x) = 0.5x about the x-axis.

19
Homework #2 – Washer Method & Different axis P.247 – 249: 7,9,11,14

20
Volume with known base The base of a solid is given by x^2 + y^2 = 4. Each slice of the solid perpendicular to the x- axis is a square. Find the volume of the solid.

21
Homework #3 – Different axis & known base P.249: 15,16,18,19

Similar presentations

OK

More on Volumes & Average Function Value. Average On the last test (2), the average of the test was: FYI - there were 35 who scored a 9 or 10, which means.

More on Volumes & Average Function Value. Average On the last test (2), the average of the test was: FYI - there were 35 who scored a 9 or 10, which means.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on exchange traded funds Ppt on otto cycle free download Disaster management ppt on uttarakhand Best ppt on sustainable development Ppt on history of computer generations Ppt on positive thinking Ppt on social impact of information technology Ppt on emotional intelligence for students Ppt on safe abortion Ppt on fdi in retail sector 2011