7.1 Area of a Region Between Two Curves

Slides:

Advertisements

Similar presentations

Area between curves. How would you determine the area between two graphs?

Advertisements

Notes Over 6.4 Graph Sine, Cosine Functions Notes Over 6.4 Graph Sine, Cosine, and Tangent Functions Equation of a Sine Function Amplitude Period Complete.

Problem of the Day. Section 4.5: Graphs of Sine and Cosine Functions. Pages What you should learn Sketch the graphs of basic sine and cosine.

Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.

Graphs of Inverse Functions. Inverse Sine Function The horizontal line test shows that the sine function is not one-to-one and has no inverse function.

7.1 Area of a Region Between Two Curves.

AP Calculus Ms. Battaglia

Do Now: p.381: #8 Integrate the two parts separately: Shaded Area =

In this section, we will investigate the process for finding the area between two curves and also the length of a given curve.

4.7 Inverse Trig Functions

Using Transformations to Graph the Sine and Cosine Curves The following examples will demonstrate a quick method for graphing transformations of.

Section 7.2a Area between curves.

Infinite Limits Determine infinite limits from the left and from the right. Find and sketch the vertical asymptotes of the graph of a function.

Section 15.3 Area and Definite Integral

Asymptotes Objective: -Be able to find vertical and horizontal asymptotes.

6.1 Areas Between Curves 1 Dr. Erickson. 6.1 Areas Between Curves2 How can we find the area between these two curves? We could split the area into several.

Which 3 functions DO NOT have all Real #’s as their domain?

P roblem of the Day - Calculator Let f be the function given by f(x) = 3e 3x and let g be the function given by g(x) = 6x 3. At what value of x do the.

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.

The Fundamental Theorem of Calculus

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.

Area of a Region Between Two Curves

PHASE SHIFTS AND VERTICAL SHIFTS I can identify the transformations made to the Sine and Cosine graph. 5.4 I can construct the Sine and Cosine.

Section 4.5 Graphs of Sine and Cosine. Sine Curve Key Points:0 Value: π 2π2π π 2π2π 1.

Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern.

Module 6.4 Graphing Sine and Cosine Functions with Different Amplitudes and Periods.

Notes Over 14.1 Graph Sine, Cosine, and Tangent Functions.

Applications of Integration 7 Copyright © Cengage Learning. All rights reserved.

Section 4.7 Inverse Trigonometric Functions. Helpful things to remember. If no horizontal line intersects the graph of a function more than once, the.

QUIZ PRACTICE Trigonometric Angles Graphing Sine and Cosine

7 Applications of Integration

Area of a Region Between Two Curves (7.1)

5.6 Phase Shift; Sinusoidal Curve Fitting

Solids of Revolution Shell Method

Linear Inequalities and Systems of Linear Inequalities

Solids of Revolution Shell Method

Area Between Two Curves

Section 5.1 Area Between Curves.

Objective: Graphs of sine and cosine functions with translations.

Horizontal Line Test.

Area Bounded by Curves sin x cos x.

Sketch the region enclosed by {image} and {image}

Sketch the region enclosed by {image} and {image}

Chapter 4: Lesson 4.5 Graphs of Sine and Cosine Functions

Area of a Region Between Two Curves (7.1)

Area Between Two Curves

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

Notes Over 6.4 Graph Sine, Cosine Functions.

6.2a DISKS METHOD (SOLIDS OF REVOLUTION)

Section 7.1 Day 1-2 Area of a Region Between Two Curves

Section 6.1: More About Areas

Find the area of the shaded region

Applications of Integration

7 Applications of Integration

Sec 6.1: AREAS BETWEEN CURVES

Estimate the area from 0 to 5 under the graph of {image} using five approximating rectangles and right endpoints

Graphs of Sine and Cosine: Sinusoids

Section 4.5 Graphs of Sine and Cosine Functions

7.1 Area of a Region Between Two Curves.

Graphing: Sine and Cosine

8.3 – Model Periodic Behavior

Warm-up: For the following equation, give the required values and graph. For the shifts, give direction as well as units of translation. If there is.

7 Applications of Integration

Intersection Method of Solution

Estimate the area from 0 to 5 under the graph of {image} using five approximating rectangles and right endpoints

2.5 Basic Differentiation Properties

Area and Arc Length in Polar Coordinates

Presentation transcript:

7.1 Area of a Region Between Two Curves

Region Between Two Curves

Finding the Area of a Region Between Two Curves Find the area of the region bounded by the graphs of

A Region Lying Between Two Intersecting Graphs Find the area of the region bounded by the graphs

A Region Lying Between Two Intersecting Graphs The sine and cosine curves intersect infinitely many times, bounding regions of equal area. Find the area of one of these regions.

Curves that Intersect at More Than Two Points Find the area of the region between the graphs of

Horizontal Representative Rectangles Find the area of the region bounded by the graphs of