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Shay10825

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Hi everyone. I would really appreciate it if someone could check my work. I was really unsure on how to do some of these. I'm sorry it is so long.

1.) Let R denote the region between the curves y=x^-1 and y=x^-2 over the interval 1<= x <= 10.

a. Set up an integral for the area of R.

My answer: 1.403

b. Find x-bar, the x coordinate of the centroid of R.

My answer: 4.775

c. Set up and evaluate an integral for the volume of revolution of the solid generated when R is revolved about

i. the x-axis

My answer: 1.781

ii. the y-axis

My answer: infinity

2.) The length of a cable is 50 and the weight is 10. A portion of length 40 was hanging over the edge of a tall building and was pulled to the top. How much work was done?

My answer: 3920

3.) Let C denote the curve y= x(4-x), where 0<= x <= 4. Set up the integral for the following. In this case, do not evaluate the integrals.

a. the length of C

My answer: integral from 0 to 4 of sqrt[ 1+ (4-2x)^2] dx

b. the area of the surface generated when C is revolved about

i. the x-axis

My answer: 2pi *integral from 0 to 4 of x(4-x)*sqrt[1+ (4-2x)^2] dx

ii. the y-axis

My answer: 2pi* integral from 0 to 4 of [sqrt(4-y) -2] *sqrt[1+ (-2*sqrt(4-y))^-2] dy

4.) A tank has the shape of a trapezoidal prism. The top is horizontal and the two ends are vertical. The length is 4. The height is 2. The top is a 3-by-4 rectangle. Viewed from an end, the tank looks like the trapezoid shown in the figure below. Assume the tank contains a liquid to a depth of 1. Take the density of the liquid to be p.

a. Set up, but do not evaluate, an integral for the work required to pump the liquid to the top of the tank.

My answer: W= p*integral from 0 to 2 of 4 dy

b. Set up, but for not evaluate, an integral for the fluid force against one end of the tank.

My answer: F= integral from 0 to 4 of p(24) dx

http://img361.imageshack.us/img361/559/calctest3nq.png [Broken]

Thank you

1.) Let R denote the region between the curves y=x^-1 and y=x^-2 over the interval 1<= x <= 10.

a. Set up an integral for the area of R.

My answer: 1.403

b. Find x-bar, the x coordinate of the centroid of R.

My answer: 4.775

c. Set up and evaluate an integral for the volume of revolution of the solid generated when R is revolved about

i. the x-axis

My answer: 1.781

ii. the y-axis

My answer: infinity

2.) The length of a cable is 50 and the weight is 10. A portion of length 40 was hanging over the edge of a tall building and was pulled to the top. How much work was done?

My answer: 3920

3.) Let C denote the curve y= x(4-x), where 0<= x <= 4. Set up the integral for the following. In this case, do not evaluate the integrals.

a. the length of C

My answer: integral from 0 to 4 of sqrt[ 1+ (4-2x)^2] dx

b. the area of the surface generated when C is revolved about

i. the x-axis

My answer: 2pi *integral from 0 to 4 of x(4-x)*sqrt[1+ (4-2x)^2] dx

ii. the y-axis

My answer: 2pi* integral from 0 to 4 of [sqrt(4-y) -2] *sqrt[1+ (-2*sqrt(4-y))^-2] dy

4.) A tank has the shape of a trapezoidal prism. The top is horizontal and the two ends are vertical. The length is 4. The height is 2. The top is a 3-by-4 rectangle. Viewed from an end, the tank looks like the trapezoid shown in the figure below. Assume the tank contains a liquid to a depth of 1. Take the density of the liquid to be p.

a. Set up, but do not evaluate, an integral for the work required to pump the liquid to the top of the tank.

My answer: W= p*integral from 0 to 2 of 4 dy

b. Set up, but for not evaluate, an integral for the fluid force against one end of the tank.

My answer: F= integral from 0 to 4 of p(24) dx

http://img361.imageshack.us/img361/559/calctest3nq.png [Broken]

Thank you

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