Explanation 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: The given functions are y = x 3 − 3 x 2 + x + 2 and y = − x 2 + 4 x + 2 . Use the online graphing calculator and sketch the graph of the given functions y = x 3 − 3 x 2 + x + 2 and y = − x 2 + 4 x + 2 is as shown in below Figure 1. From the Figure 1, it is observed that the functions are y = x 3 − 3 x 2 + x + 2 and y = − x 2 + 4 x + 2 intersects at the points ( − 1 , 3 ) , ( 0 , 2 ) , and ( 3 , 5 ) . It is noted that the function y = x 3 − 3 x 2 + x + 2 is greater than the function y = − x 2 + 4 x + 2 over the interval [ − 1 , 0 ] and the function y = − x 2 + 4 x + 2 is greater than the function y = x 3 − 3 x 2 + x + 2 over the interval [ 0 , 3 ] . By the above mentioned theorem, the area of the shaded region is computed as follows. A = ∫ − 1 0 ( x 3 − 3 x 2 + x + 2 − ( − x 2 + 4 x + 2 ) ) d x + ∫ 0 3 ( ( − x 2 + 4 x + 2 ) − ( x 3 − 3 x 2 + x + 2 ) ) d x = ∫ − 1 0 (

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Question

Chapter 6.1, Problem 68E

To determine

To find: The area bounded by the graphs of y=x3−3x2+x+2 and y=−x2+4x+2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.1, Problem 67E

Chapter 6.1, Problem 69E

Students have asked these similar questions

= 12:02 WeBWorK / 2024 Fall Rafeek MTH23 D02 / 9.2 Testing the Mean mu / 3 38 WEBWORK Previous Problem Problem List Next Problem 9.2 Testing the Mean mu: Problem 3 (1 point) Test the claim that the population of sophomore college students has a mean grade point average greater than 2.2. Sample statistics include n = 71, x = 2.44, and s = 0.9. Use a significance level of a = 0.01. The test statistic is The P-Value is between : The final conclusion is < P-value < A. There is sufficient evidence to support the claim that the mean grade point average is greater than 2.2. ○ B. There is not sufficient evidence to support the claim that the mean grade point average is greater than 2.2. Note: You can earn partial credit on this problem. Note: You are in the Reduced Scoring Period. All work counts for 50% of the original. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. . Oli wwm01.bcc.cuny.edu

>tt 1:32 > trend.1m 1m (sales > summary(trend.1m) - tt) #3###23 (i) #### Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2107.220 57.997 36.332e-16 *** tt -43.500 3.067 -14.18 7.72e-15 *** > trend = ts (fitted (trend.1m), start-start (sales), freq-frequency (sales)) sales trend ###23%23 (ii) #### as.numeric((1:32 %% 4) > X > q1 > q2 > q3 > 94 = = = = - as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) == 1) 2) == == 3) == 0) > season.lm = 1m (resid (trend.1m) 0+q1 + q2 + q3 + q4) #3##23%23 (iii) #### > summary(season.1m) Coefficients: Estimate Std. Error t value Pr(>|t|) q1 -38.41 43.27 -0.888 0.38232 92 18.80 43.27 0.435 0.66719 q3 -134.78 43.27 -3.115 0.00422 ** 94 154.38 43.27 3.568 0.00132 ** > season = ts (fitted (season.lm), start=start (sales), freq=frequency (sales)) > Y X season %23%23%23%23 (iv) #### >ar (Y, aic=FALSE, order.max=1) #23%23%23%23 (v) #### Coefficients: 1 0.5704 Order selected 1 sigma 2 estimated as 9431 > ar(Y, aic=FALSE,…

Please sketch questions 1, 2 and 6

Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

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

The area bounded by the graphs of y = x 3 − 3 x 2 + x + 2 and y = − x 2 + 4 x + 2 .

Solution Summary: The area of the shaded region is 11.833 Sq. units.

To find: The area bounded by the graphs of y=x3−3x2+x+2 and y=−x2+4x+2.

Want to see the full answer?

Chapter 6 Solutions