7.1 – 7.3 Review Area and Volume. The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Determine when the particle is moving.

Slides:

Advertisements

Similar presentations

Section Volumes by Slicing

Advertisements

Volume by Parallel Cross Section; Disks and Washers

DO NOW: Find the volume of the solid generated when the

Disks, Washers, and Cross Sections Review

Section Volumes by Slicing

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.

Volumes – The Disk Method Lesson 7.2. Revolving a Function Consider a function f(x) on the interval [a, b] Now consider revolving that segment of curve.

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.

7.1 Area Between 2 Curves Objective: To calculate the area between 2 curves. Type 1: The top to bottom curve does not change. a b f(x) g(x) *Vertical.

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.

Section 6.2.  Solids of Revolution – if a region in the plane is revolved about a line “line-axis of revolution”  Simplest Solid – right circular cylinder.

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.

SECTION 7.3 Volume. VOLUMES OF AN OBJECT WITH A KNOWN CROSS-SECTION  Think of the formula for the volume of a prism: V = Bh.  The base is a cross-section.

Integral calculus XII STANDARD MATHEMATICS. Evaluate: Adding (1) and (2) 2I = 3 I = 3/2.

7.3 Volumes Quick Review What you’ll learn about Volumes As an Integral Square Cross Sections Circular Cross Sections Cylindrical Shells Other Cross.

Finding Volumes.

Volume of a Solid by Cross Section Section 5-9. Let be the region bounded by the graphs of x = y 2 and x=9. Find the volume of the solid that has as its.

Review: Volumes of Revolution. x y A 45 o wedge is cut from a cylinder of radius 3 as shown. Find the volume of the wedge. You could slice this wedge.

Section Volumes by Slicing

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2006.

6036: Area of a Plane Region AB Calculus. Accumulation vs. Area Area is defined as positive. The base and the height must be positive. Accumulation can.

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

Chapter 7 Quiz Calculators allowed. 1. Find the area between the functions y=x 2 and y=x 3 a) 1/3 b) 1/12 c) 7/12 d) 1/4 2. Find the area between the.

Volume of Cross-Sectional Solids

Chapter 7 AP Calculus BC. 7.1 Integral as Net Change Models a particle moving along the x- axis for t from 0 to 5. What is its initial velocity? When.

A honey bee makes several trips from the hive to a flower garden. The velocity graph is shown below. What is the total distance traveled by the bee?

Solids of Revolution Disk Method

Volume: The Disc Method

Review 7 Area between curves for x Area between curves for y Volume –area rotated –disks for x and y Volume – area rotated – washers for x and y Volume.

Let R be the region bounded by the curve y = e x/2, the y-axis and the line y = e. 1)Sketch the region R. Include points of intersection. 2) Find the.

Section 7.1: Integral as Net Change

8.1 A – Integral as Net Change Goal: Use integrals to determine an objects direction, displacement and position.

Volumes Using Cross-Sections Solids of Revolution Solids Solids not generated by Revolution Examples: Classify the solids.

Finding Volumes Chapter 6.2 February 22, In General: Vertical Cut:Horizontal Cut:

Volumes Lesson 6.2.

THIS IS With Host... Your Derivatives Tangent Lines & Rates of Change Applications of derivatives Integration Applications of.

Volumes by Slicing 7.3 Solids of Revolution.

Aim: Shell Method for Finding Volume Course: Calculus Do Now: Aim: How do we find volume using the Shell Method? Find the volume of the solid that results.

Volumes by Slicing. disk Find the Volume of revolution using the disk method washer Find the volume of revolution using the washer method shell Find the.

6.2 Volumes on a Base.

Section Volumes by Slicing 7.3 Solids of Revolution.

Quick Review & Centers of Mass Chapter 8.3 March 13, 2007.

6.2 Setting Up Integrals: Volume, Density, Average Value Mon Dec 14 Find the area between the following curves.

Ch. 8 – Applications of Definite Integrals 8.3 – Volumes.

Volume Find the area of a random cross section, then integrate it.

Ch. 8 – Applications of Definite Integrals 8.1 – Integral as Net Change.

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 =

SECTION 7-3-C Volumes of Known Cross - Sections. Recall: Perpendicular to x – axis Perpendicular to y – axis.

 The volume of a known integrable cross- section area A(x) from x = a to x = b is  Common areas:  square: A = s 2 semi-circle: A = ½  r 2 equilateral.

6.3 Volumes by Cylindrical Shells. Find the volume of the solid obtained by rotating the region bounded,, and about the y -axis. We can use the washer.

C.2.5b – Volumes of Revolution – Method of Cylinders Calculus – Santowski 6/12/20161Calculus - Santowski.

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

7.2 Volume: The Disk Method (Day 3) (Volume of Solids with known Cross- Sections) Objectives: -Students will find the volume of a solid of revolution using.

Extra Review Chapter 7 (Area, Volume, Distance). Given that is the region bounded by Find the following  Area of  Volume by revolving around the x-axis.

DO NOW: v(t) = e sint cost, 0 ≤t≤2∏ (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particles displacement.

7-2 SOLIDS OF REVOLUTION Rizzi – Calc BC. UM…WHAT?  A region rotated about an axis creates a solid of revolution  Visualization Visualization.

Motion Graphs Position-Time (also called Distance-Time or Displacement-Time) d t At rest.

Finding Volumes.

The Shell Method Section 7.3.

Cross Sections Section 7.2.

Volume of Solids with Known Cross Sections

Applications Of The Definite Integral

Warm Up Find the volume of the following shapes (cubic inches)

Chapter 6 Cross Sectional Volume

The integral represents the area between the curve and the x-axis.

Section Volumes by Slicing

Warm Up Find the volume of the following 3 dimensional shapes.

AP problem back ch 7: skip # 7

Presentation transcript:

7.1 – 7.3 Review Area and Volume

The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Determine when the particle is moving to the right, to the left, and stopped.

2.The velocity in m/sec of a particle moving along the x-axis is given by the function Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position at the end of the given time interval?

The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Find the total distance traveled by the particle.

4.A car accelerates from rest at the rate of mph per second for 16 seconds. What is its velocity after 16 seconds?

5.In town A, the birth rate is given by where t is the number of years since In town B, the birth rate is given by where t is the number of years since How many more births are there in town B than in town A during the 1990s (from t = 0 to t = 10)? Round your answer to the nearest whole number.

6.It took 1930 J of work to stretch a spring from its natural length of 1 m to a length of 3 m. Find the spring's force constant.

Find the area of the shaded region.

Find the area of the regions enclosed by the lines and curves.

Find the area enclosed by the given curves.

Find the area of the regions enclosed by the lines and curves.

Find the area of the region(s) enclosed by the given curves.

Find the volume of the described solid. 13.The solid lies between planes perpendicular to the x - axis at x = - 3 and x = 3 and. The cross sections perpendicular to the x - axis between these planes are squares whose bases run from the semicircle to the semicircle

Find the volume of the solid generated by revolving the shaded region about the given axis. 14. About the y-axis

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the.

Find the volume of the solid generated by revolving the region about the y-axis. 17.The region in the first quadrant bounded on the left by on the right by the line x = 2, and below by the x - axis.

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x - axis.