Presentation is loading. Please wait.

Presentation is loading. Please wait.

Thursday, February 11, 2016MAT 146. Thursday, February 11, 2016MAT 146.

Published byBerenice Armstrong Modified over 8 years ago

Similar presentations

Presentation on theme: "Thursday, February 11, 2016MAT 146. Thursday, February 11, 2016MAT 146."— Presentation transcript:

1 Thursday, February 11, 2016MAT 146

2 Thursday, February 11, 2016MAT 146

3 Thursday, February 11, 2016MAT 146

4 Thursday, February 11, 2016MAT 146

5 Thursday, February 11, 2016MAT 146

6 Thursday, February 11, 2016MAT 146

7 Thursday, February 11, 2016MAT 146

8 Thursday, February 11, 2016MAT 146 Improper Algebraic Fractions? Unfactorable Quadratics? Repeated Linear Factors?

9 Thursday, February 11, 2016MAT 146 Consider the first-quadrant region R with borders y = sin(x)y = 0andx = π / 2 (A)Sketch region R on the xy-plane. (A)Calculate the exact area of R. Show evidence to support your solution. (B)Set up, but do not calculate, a definite integral to represent the volume of the solid created when R is revolved around the y-axis.

10 Thursday, February 11, 2016MAT 146 Consider the first-quadrant region R with borders y = sin(x)y = 0andx = π / 2 (A)Sketch region R on the xy-plane.

11 Thursday, February 11, 2016MAT 146 Consider the first-quadrant region R with borders y = sin(x)y = 0andx = π / 2 B.Calculate the exact area of R. Show evidence to support your solution.

12 Thursday, February 11, 2016MAT 146 Consider the first-quadrant region R with borders y = sin(x)y = 0andx = π / 2 C.Set up, but do not calculate, a definite integral to represent the volume of the solid created when R is revolved around the y-axis. Shells: Washers:

Download ppt "Thursday, February 11, 2016MAT 146. Thursday, February 11, 2016MAT 146."

Similar presentations

Find the exact volume of the solid formed by revolving the region enclosed by the following functions around the x-axis. Specify whether you are using.

Find the exact volume of the solid formed by revolving the region enclosed by the following functions around the x-axis. Specify whether you are using.
- Volumes of a Solid The volumes of solid that can be cut into thin slices, where the volumes can be interpreted as a definite integral.

- Volumes of a Solid The volumes of solid that can be cut into thin slices, where the volumes can be interpreted as a definite integral.
The Disk Method (7.2) April 17th, 2012. I. The Disk Method Def. If a region in the coordinate plane is revolved about a line, called the axis of revolution,

The Disk Method (7.2) April 17th, I. The Disk Method Def. If a region in the coordinate plane is revolved about a line, called the axis of revolution,
Section 6.2: Volumes Practice HW from Stewart Textbook (not to hand in) p. 457 # 1-13 odd.

Section 6.2: Volumes Practice HW from Stewart Textbook (not to hand in) p. 457 # 1-13 odd.
6.2 - Volumes. Definition: Right Cylinder Let B 1 and B 2 be two congruent bases. A cylinder is the points on the line segments perpendicular to the bases.

6.2 - Volumes. Definition: Right Cylinder Let B 1 and B 2 be two congruent bases. A cylinder is the points on the line segments perpendicular to the bases.
4/30/2015 Perkins AP Calculus AB Day 4 Section 7.2.

4/30/2015 Perkins AP Calculus AB Day 4 Section 7.2.
The Shell Method Volumes by Cylindrical Shells By Christine Li, Per. 4.

The Shell Method Volumes by Cylindrical Shells By Christine Li, Per. 4.
Applications of Integration

Applications of Integration
Find the volume when the region enclosed by y = x and y = x 2 is rotated about the x-axis? - creates a horn shaped cone - area of the cone will be the.

Find the volume when the region enclosed by y = x and y = x 2 is rotated about the x-axis? - creates a horn shaped cone - area of the cone will be the.
TOPIC APPLICATIONS VOLUME BY INTEGRATION. define what a solid of revolution is decide which method will best determine the volume of the solid apply the.

TOPIC APPLICATIONS VOLUME BY INTEGRATION. define what a solid of revolution is decide which method will best determine the volume of the solid apply the.
Volume. Find the volume of the solid formed by revolving the region bounded by the graphs y = x 3 + x + 1, y = 1, and x = 1 about the line x = 2.

Volume. Find the volume of the solid formed by revolving the region bounded by the graphs y = x 3 + x + 1, y = 1, and x = 1 about the line x = 2.
S OLIDS OF R EVOLUTION 4-G. Disk method Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate.

S OLIDS OF R EVOLUTION 4-G. Disk method Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate.
Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146.

Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146.
TOPIC TECHNIQUES OF INTEGRATION. 1. Integration by parts 2. Integration by trigonometric substitution 3. Integration by miscellaneous substitution 4.

TOPIC TECHNIQUES OF INTEGRATION. 1. Integration by parts 2. Integration by trigonometric substitution 3. Integration by miscellaneous substitution 4.
Thursday, January 22, 2015MAT 146. Thursday, January 22, 2015MAT 146 1. Calculate the area between the graphs of y = 2x 3 – 1 and y = x – 1 for 1 ≤ x.

Thursday, January 22, 2015MAT 146. Thursday, January 22, 2015MAT Calculate the area between the graphs of y = 2x 3 – 1 and y = x – 1 for 1 ≤ x.
Wednesday, February 4, 2015MAT 146. Wednesday, February 4, 2015MAT 146.

Wednesday, February 4, 2015MAT 146. Wednesday, February 4, 2015MAT 146.
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 7.2 B Volumes by the Washer Method Limerick Nuclear Generating Station,

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, B Volumes by the Washer Method Limerick Nuclear Generating Station,
7.3 Volumes by Cylindrical Shells

7.3 Volumes by Cylindrical Shells
MTH 252 Integral Calculus Chapter 7 – Applications of the Definite Integral Section 7.3 – Volumes by Cylindrical Shells Copyright © 2006 by Ron Wallace,

MTH 252 Integral Calculus Chapter 7 – Applications of the Definite Integral Section 7.3 – Volumes by Cylindrical Shells Copyright © 2006 by Ron Wallace,
1 st order linear differential equation: P, Q – continuous. Algorithm: Find I(x), s.t. by solving differential equation for I(x): then integrate both sides.

1 st order linear differential equation: P, Q – continuous. Algorithm: Find I(x), s.t. by solving differential equation for I(x): then integrate both sides.

Similar presentations

Ads by Google