Question: Show that if we rotate the curve y = e x/2 + e -x/2 about the x-axis, the area of the resulting surface is the

Show that if we rotate the curve 

y = ex/2 + e-x/2

 about the x-axis, the area of the resulting surface is the same value as the enclosed volume for any interval a < x < b.

Step by Step Solution

★★★★★

3.51 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

y e 2 e22 y e 1e 1 y 1 e e2 1 e e e e e e e1 If we rotate the ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

We have seen in this section that systems of linear equations have limited possibilities for solution sets, and we will shortly prove Theorem PSSLS that describes these possibilities exactly. This...

Q:

Show that if we want to approximate the sum of the series So that the error is less than 5 in the ninth decimal place, then we need to add more than 1011,301 terms! 2 n1.001

Q:

Show that if we let = M/N in Theorem 5.7, the mean and the variance of the hypergeometric distribution can be written as = n and 2 = n(1 ) N n / N 1 . How do these results tie in with the...

Q:

1. 3 2 Consider the function f(x) = x - 3x - 9x + 10, x (a) . Find the equation of the straight line passing through the maximum and minimum points of the graph y = f(x). (4) (b) Show that the point...

Q:

Find the length of the arc of the semicubical parabola y? = x between the points (1, 1) and (16, 64). (16, 64) = x3 (1, 1) SOLUTION For the top half of the curve we have y = x3/2 dy = 3 dx Amazing...

Q:

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

Q:

Can you please help me with problems 8 and 26 from the last photo. Thanks so much! :) . AT&T 10:23 PM 01 9% SECTION 11.3 Polar Coordinates 637 penises 31-38. use Eq. (4) to compute the surface area...

Q:

Can you help me with problems 28, 32, 36 from the last page? Thanks so much! . AT&T 10:23 PM 01 9% SECTION 11.3 Polar Coordinates 637 penises 31-38. use Eq. (4) to compute the surface area of the...

Q:

1 Exercise 3: Lift and Airfoils The first part of this week's assignment is to choose and research a reciprocating engine powered (i.e. propeller type) aircraft. You will further use your selected...

Q:

The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the...

Q:

Analyze the role of religion in shaping political and social structures throughout history, using specific examples from different cultures and time periods.

Q:

A two-port network is known to have the following parameters: If a 2-A current source is connected to the input terminals as shown in figure, find the voltage across this current source. a. 36 V b....

Q:

7. LO.3 Indicate whether each of the following items should be allocated or apportioned by the taxpayer in computing state corporate taxable income. Assume that the state follows the general rules of...

Q:

12. What was the purpose of the Sarbanes-Oxley Act of 2002? (L06)

Q:

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. The integral E kr 3 dz dr dc represents the...

Q:

Calculate the iterated integral. SLL 6xyz dz dx dy 10 JI

Q:

Sketch the region whose area is given by the integral and evaluate the integral. L r dr de (2 sine T/2 Jo

Q:

Use following information to calculate Net Operating Profit After Tax (NOPAT) for Walmart for 2011: A. $16,487 B. $17,222 C. $29,435 D. $13,987 E. $12,976 WALMART INCOME STATEMENT 2010 TOTAL REVENUES...

Q:

Please show cell references/formulas. Thank you. Suppose that in January 2006, Kenneth Cole Productions had EPS of $1.65 and a book value of equity of $12.05 per share. Complete the steps below using...

Q:

5. MO Ltd. is considering a five-year project to expand its production efficiency. Building a new plant for $1,000,000 at the beginning of the project is estimated to result in annual sales quantity...