11.) Find the arc length of the curve given by y (4on the interval [1, 81. (ome:-)3/2(4x2/3oon the interval [1, 8]. (ans: 9)Find the arc length of the curve given by x-2 (y - 1)3/2 where 16 s y s 25. (ans: 122/3)13.) Find the arc length of the curve given byyx where 1 s x 4. (ans: 8718)14.) Find the area of the surface of revolution of the region by yvx whereabout theX-axis. (ans: (1917)3where [0,2] about theFind the area of the surface of revolution of the region by yX-axis. (ans: a)15.)16,) Find the area of the surface of revolution of the region by y 2 on [o,v2] about they-axis. (ans: 13)

Question

Number 12

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Step 1

Arc length of the curve:

Arc length is the distance between two points along a section of a curve.

The length of the continuous function x = f(y) on the interval [a,b] is given below:

Step 2

Find the derivate (dx/dy) of x = (2/3)*(y–1)3/2:

The given function is x = (2/3)*(y–1)3/2.

The derivate (dx/dy) of x = (2/3)*(y–1)3/2 is obtained as (y – 1)1/2 from the calculation given below:

Step 3

Find the arc length of the curve x = (2/3)*(y–1)3/2 on the interval [16, 25]:

The derivate (dx/dy) of the continuous function is (dx/dy) = .

It is g...

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