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 functions are y = x 3 − x 2 + 2 and y = − x 3 + 8 x − 2 . Using online graphing calculator, sketch the graph of the given functions y = x 3 − x 2 + 2 and y = − x 3 + 8 x − 2 is as shown below in Figure 1. From Figure 1, it is observed that the functions y = x 3 − x 2 + 2 and y = − x 3 + 8 x − 2 intersect at the points ( 0.5 , 1.875 ) ( − 2 , − 10 ) , and ( 2 , 6 ) . By the above mentioned theorem, the area of the shaded region is computed as follows. A = ∫ − 2 0.5 ( x 3 − x 2 + 2 − ( − x 3 + 8 x − 2 ) ) d x + ∫ 0.5 2 ( − x 3 + 8 x − 2 − ( x 3 − x 2 + 2 ) ) d x = − ∫ − 2 0.5 ( − 2 x 3 + x 2 + 8 x − 4 ) d x + ∫ 0.5 2 ( − 2 x 3 + x 2 + 8 x − 4 ) d x = − [ − x 4 2 + x 3 3 + 4 x 2 − 4 x ] − 2 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

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

Publisher: PEARSON

See similar textbooks

Question

Chapter 6.1, Problem 71E

To determine

To find: The area bounded by the graphs of y=x3−x2+2 and y=−x3+8x−2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.1, Problem 70E

Chapter 6.1, Problem 72E

Students have asked these similar questions

>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

QUESTION 18 - 1 POINT Jessie is playing a dice game and bets $9 on her first roll. If a 10, 7, or 4 is rolled, she wins $9. This happens with a probability of . If an 8 or 2 is rolled, she loses her $9. This has a probability of J. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on her first roll. Round to the nearest cent if necessary. Do not round until the final calculation. Provide your answer below:

Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th 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. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...

Knowledge Booster

The area bounded by the graphs of y = x 3 − x 2 + 2 and y = − x 3 + 8 x − 2 .

To find: The area bounded by the graphs of y=x3−x2+2 and y=−x3+8x−2.

Want to see the full answer?

Chapter 6 Solutions