1) the base of a certain solid is the region enclosed by y=1/x, y=0, x=1 and x=3
ID: 2963035 • Letter: 1
Question
1) the base of a certain solid is the region enclosed by y=1/x, y=0, x=1 and x=3. every cross section perpindicular to the x axis is an isosceles right triangle with its hypotenuse across the base. Find the volume of the solid
2) find the volume of the solid of revolution generated by revolving about the y axis the region bounded by y=2x^2 from x=0 to x=1 and y=0 using the washer method
3)the arc of y= 2/3 (x^2 +1)^3/2 from x=0 to x=4 is rotated about the y- axis. find the area of the surface generated
4) the base of a certain solid is the region enclosed by y=x^2 , y=0 and x=2. every cross section perpindicular to the x-axis is a semicircle with its diameter across the base. Find the volume fo the solid.
P.S. these are the only questions I have left in a 50+ question assignment that is due soon so the faster the better and all help is appreciated thank you!!!!! :)
Explanation / Answer
These are too many questions for 300 points.
Here is the first
The base of the solid is 1/x. The height is sqrt 2/2x So the area is 1/2 bh or sqrt 2/4x^2
We integrate from x=1 to x=3
Antiderivative is - sqrt 2/4x
From 1 to 3 we have -sqrt2/12 + sqrt2/4= sqrt 2/6
Post the others separately and I'll do them.
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