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Arc length of a Curve

How does the length of the curve x=t^2, y=t^3, [0,2] come out to be 3/4 + (ln2)/2?

Subject:

Math

Topic:

Calculus

Posting ID:

6874

OTA ID:

101298

View Details $1.99 Download Add to Cart

Surface area of revolution

How do I find the surface area obtained by revolving the curve y=x-1 from x=1 to x=4 about the line x= -1?

Subject:

Math

Topic:

Calculus

Posting ID:

6877

OTA ID:

102846

View Details $1.99 Download Add to Cart

Calculus: Integration by Parts

I need to find the integral of x^2 sin 3x dx. My text says that the answer should be 1/27[6x sin 3x -(9x^2-2) cos 3x] + c I'm hoping that someone can show me how to get to this answer, and would appreciate any advice for integration by parts.

Subject:

Math

Topic:

Calculus

Posting ID:

6883

OTA ID:

103642

View Details $1.99 Download Add to Cart

Volume of water poured in to bowl with iron ball.

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Subject:

Math

Topic:

Calculus

Posting ID:

6918

OTA ID:

102959

View Details $1.99 Download Add to Cart

A problem dealing with volume of revolution

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Subject:

Math

Topic:

Calculus

Posting ID:

6930

OTA ID:

102959

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