Review 6.1, 6.2, 6.4.

Slides:

Advertisements

Similar presentations

- 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.

Advertisements

Section Volumes by Slicing

Adapted by Mrs. King from

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.

Integral Calculus One Mark Questions. Choose the Correct Answer 1. The value of is (a) (b) (c) 0(d)  2. The value of is (a) (b) 0 (c) (d) 

Volume: The Shell Method Lesson 7.3. Find the volume generated when this shape is revolved about the y axis. We can’t solve for x, so we can’t use a horizontal.

Section 7.2 Solids of Revolution. 1 st Day Solids with Known Cross Sections.

Applications Of The Definite Integral The Area under the curve of a function The area between two curves The Volume of the Solid of revolution.

7.1 Area of a Region Between Two Curves.

Area Between Two Curves 7.1. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the.

Do Now: #10 on p.391 Cross section width: Cross section area: Volume:

Chapter 5: Integration and Its Applications

Volumes of Revolution The Shell Method Lesson 7.3.

1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :

How to solve an AP Calculus Problem… Jon Madara, Mark Palli, Eric Rakoczy.

Sketch the region bounded by the graph of the equations and determine the area of the region Y = sinx y = cosxπ/4≤ x ≤ 5π/4.

6.3 Volumes of Revolution Tues Dec 15 Do Now Find the volume of the solid whose base is the region enclosed by y = x^2 and y = 3, and whose cross sections.

Volume: The Disk Method. Some examples of solids of revolution:

8.1 Arc Length and Surface Area Thurs Feb 4 Do Now Find the volume of the solid created by revolving the region bounded by the x-axis, y-axis, and y =

6.3 Volumes of Revolution Fri Feb 26 Do Now Find the volume of the solid whose base is the region enclosed by y = x^2 and y = 3, and whose cross sections.

Calculus 6-R Unit 6 Applications of Integration Review Problems.

Volumes of Solids of Rotation: The Disc Method

7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington(Photo not taken by Vickie Kelly)

6.4 Cylindrical Shells Thurs Dec 17 Revolve the region bounded by y = x^2 + 2, the x-axis, the y-axis, and x = 2 about the line x = 2.

Solids of Revolution Revolution about x-axis. What is a Solid of Revolution? Consider the area under the graph of from x = 0 to x = 2.

The Disk Method (7.2) February 14th, 2017.

FINDING VOLUME USING DISK METHOD & WASHER METHOD

Volume: The Disk Method

Solids of Revolution Shell Method

Solids of Revolution Shell Method

7.2 Volume: The Disk Method

Lesson 49 – Volumes of Revolution

Area Between Two Curves

The Shell Method Section 7.3.

Finding the Volume of a Solid of Revolution

1.) Set up the integral to find the area of the shaded region

Finding Volumes Disk/Washer/Shell

Review of Area: Measuring a length.

Volumes of Revolution Disks and Washers

Determine f(x) from the table: x f(x) -1 0

Finding Volumes Disk/Washer/Shell

Volumes of Revolution The Shell Method

6.4 Integration of exponential reciprocal of x and some trig functions

Volumes – The Disk Method

Volume: The Shell Method

Volumes of Solids of Revolution

Length of Curves and Surface Area

Chapter 7.2: Volume The Disk Method The Washer Method Cross-sections

9.4: Finding Volume using Washer Method

7.3 Volume: The Shell Method

6.2 Volumes If a region in the plane is revolved about a line, the resulting solid is called a solid of revolution, the line is called the axis of revolution.

An Interlude….

Warm up Find the area of surface formed by revolving the graph of f(x) = 6x3 on the interval [0, 4] about the x-axis.

Applications Of The Definite Integral

6.2a DISKS METHOD (SOLIDS OF REVOLUTION)

Section 7.2 Day 1 Disk method

Area & Volume Chapter 6.1 & 6.2 February 20, 2007.

Volumes of Revolution The Shell Method

Section 5.3: Finding the Total Area

Warm Up Draw the graph and identify the axis of rotation that

AP Calculus AB Day 3 Section 7.2 5/7/2019 Perkins.

6.1 Areas Between Curves To find the area:

Section 7.2 Day 2 Disk Method

6.2 Solids of Revolution-Disk Method Warm Up

Section Volumes by Slicing

Warm Up Draw the graph and identify the axis of rotation that

Solids of Revolution PART DEUX: WaShErS Rita Korsunsky

Volumes of Revolution: Disk and Washer Method

of Solids of Revolution

VOLUMES BY CYLINDRICAL SHELLS

Presentation transcript:

Review 6.1, 6.2, 6.4

6.1: Sketch the region bounded by the graphs of f(x) = x2 + 2x and g(x) = x + 2. Then, find the area of the region without using a calculator.

6.1 Use a graphing utility to graph the region bounded by the graphs of f(x) = x3-2x+1, g(x) = -2x, and x = 1. Then, use the graphing utility to find the area of the region.

6.2 Find the volume of the solid generated by rotating the graphs y = x2 and y = 4x–x2 about the (a) x-axis and (b) line y = 6

6.2 Find the volume of the solid generated by rotating the region bounded by the graphs of y = 5 – x, y = 0, y = 4, and x = 0 about the y – axis.

6.4 Find the arc length of the given function over the given interval: y = [0, 1]

6.4 Find the area of the surface generated by revolving the graph of y = on the interval [1, 2] about the x-axis.