Explanation Given: The equation is y = ( x − 1 ) e x 2 ; 0 ≤ x ≤ 2 . Theorem used: If f and g are continuous and f ( x ) ≥ g ( x ) over the interval [ a , b ] , then the area bounded by y = f ( x ) and y = g ( x ) for a ≤ x ≤ b is given exactly by A = ∫ a b [ f ( x ) − g ( x ) ] d x . Calculation: Use online graphing calculator to sketch the graph of the given function y = ( x − 1 ) e x 2 in the interval [ 0 , 2 ] is as shown below in Figure 1. From Figure 1, it is observed that the graph of f ( x ) intersects the x -axis at the point ( 1 , 0 ) . The graph of f ( x ) ≤ 0 on [ 0 , 1 ] and f ( x ) ≥ 0 on [ 1 , 2 ] . By the above mentioned theorem, the area of the shaded region is computed as follows. A = ∫ 0 1 [ 0 − f ( x ) ] d x + ∫ 1 2 [ f ( x ) − 0 ] d x = ∫ 0 1 − ( x − 1 ) e x 2

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

See similar textbooks

Videos

Question

Chapter 6.3, Problem 70E

To determine

To sketch: The graph of the equation y=(x−1)ex2 and find the area between the curve and the x axis over the interval [0,2].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 69E

Chapter 6.3, Problem 71E

Students have asked these similar questions

find the zeros of the function algebraically: f(x) = 9x2 - 3x - 2

Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 119 lb 20.2° 377 lb

An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?

Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 8MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The graph of the equation y = ( x − 1 ) e x 2 and find the area between the curve and the x axis over the interval [ 0 , 2 ] .

Solution Summary: The graph of the given function y=(x-1)ex2 is as shown in Figure 1. The area between the curve and the x axis is 11.55 Sq

Videos

To sketch: The graph of the equation y=(x−1)ex2 and find the area between the curve and the x axis over the interval [0,2].

Want to see the full answer?

Chapter 6 Solutions