Question

In: Math

Write two different integrals (one with respect to x, and one with respect to y) that...

Write two different integrals (one with respect to x, and one with respect to y) that express the surface area obtained by revolving the curve y = 2√ x between the points (0,0) and (1,2) about the x-axis. Calculate the easier integral.

Solutions

Expert Solution

The given curve is,

diff wrt x,

The surface area of revolution about the x-axis is given by,

The given curve can be written as,

diff wrt y,

The surface area of revolution about the y-axis is given by,

To calculate the easier integral:

integrate wrt x,

I hope this answer helps,
Thanks,
Keep posting questions.


Related Solutions

1)Two good (x and y) are complements. The cross-price elasticity of x with respect to the...
1)Two good (x and y) are complements. The cross-price elasticity of x with respect to the price of y is a. positive. b. negative. c. zero. d. None of the above. 2) For an inferior good, the income and substitution effects a. Work together. b. Work against each other. c. Can work together or in opposition to each other depending upon their relative magnitudes. d. Always exactly cancel each other. 3) Elasticity measures a. The slope of a demand curve....
Given the equation: sin(x+y)=x+cos(y) a) Differentiate y with respect to x b) Give the equation of...
Given the equation: sin(x+y)=x+cos(y) a) Differentiate y with respect to x b) Give the equation of the line tangent to the curve of at the point (0,π/4)
Use two different ways to prove X Y + Z = (X + Z)(Y + Z)....
Use two different ways to prove X Y + Z = (X + Z)(Y + Z). a) Use pure algebraic way b) k-maps
Collect data on one response (dependent or y) variable and two different explanatory (independent or x)...
Collect data on one response (dependent or y) variable and two different explanatory (independent or x) variables. This will require a survey with three questions. For example: To predict a student’s GPA (y), you might collect data on two x variables: SAT score and age. So we would be trying to determine if there was a linear correlation between someone’s SAT score and their GPA, as well as their age and their GPA. (Note: students may not choose GPA as...
Collect data on one response (dependent or y) variable and two different explanatory (independent or x)...
Collect data on one response (dependent or y) variable and two different explanatory (independent or x) variables. This will require a survey with three questions. For example: To predict a student’s GPA (y), you might collect data on two x variables: SAT score and age. So we would be trying to determine if there was a linear correlation between someone’s SAT score and their GPA, as well as their age and their GPA. (Note: students may not choose GPA as...
Suppose two nations are identical in every respect, they produce commodity X and Y. Now nation1...
Suppose two nations are identical in every respect, they produce commodity X and Y. Now nation1 expands its production of commodity X and achieves economies of scale, then if it is possible for the two nations to trade with each other? What’s the basis for trade? What’s the pattern of production and trade? What are the gains from trade?
6.There are two assets in one portfolio, X and Y. The weight for Asset X is...
6.There are two assets in one portfolio, X and Y. The weight for Asset X is 48%. Asset X has a 50-50 chance of earning a return of 10% or 20%. Asset Y's expected return is 23% and the standard deviation is 33%. Assume the correlation coefficient between X and Y is 0.53. Calcualte the expected return of the portfolio. Calculate the standard deviation of the portfolio return.
y'=y-x^2 ; y(1)= -4 Write a MATLAB program that makes two plots of the solution to...
y'=y-x^2 ; y(1)= -4 Write a MATLAB program that makes two plots of the solution to the equation using the following values. Suggest you use nested loops instead of two different loops. Be sure to label your plots. a. x0 = 1.0, step size h = .2, number of steps n = 20. b. x0 = 1.0, step size h = .05, number of steps n = 80.
With the area between the graphs: x+y=14 x+6=y^2 Find the area two different ways First way:...
With the area between the graphs: x+y=14 x+6=y^2 Find the area two different ways First way: [a,b]integral(f(x))dx + [b,c]integral(g(x))dx = whats is a,b,c, f(x), and g(x): Second way: [a, b]integral(h(y))dy what is a, b, and h(y)
What are the partial derivatives of the equation y = 10^(0.7941log10(x)+log(0.0774)) with respect to m, x,...
What are the partial derivatives of the equation y = 10^(0.7941log10(x)+log(0.0774)) with respect to m, x, and b if the equation is equivalent to y=10^(mlog10(x)+log10(b))? Keep in mind I have not taken Calculus 3 as of yet, this is for my calculus based physics lab so that I can use the partial derivative and the uncertainty to calculate the contribution of each term to the uncertainty of the calculated variable.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT