Volume of Solid: Find Y-Axis Rot. Region

africanmasks
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Homework Statement



Find the volume of the solid formed by rotating the region enclosed by the following equations about the Y-AXIS.

y= e^(3x)+5
y=0
x=0
x= 1/2

Homework Equations


The Attempt at a Solution



I keep getting the answer wrong. I broke the problem into two parts: solved a cylinder(disk) from y= 0 to 5 and solved a washer from y=5 to e^(3/2)+5

My answer was (1.25pi) (for cylinder or disk) + (.49811372pi) (for washer)
 
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Where's your work? For the cylinder wouldn't x go from 0 to 1/2?
 
you're rotating around the y not x
 
africanmasks said:
you're rotating around the y not x

Yes, so the cylinder elements are parallel to the y axis, sometimes called "dx elements". Your natural variable for that is x.

Maybe I misunderstand your terminology. Is what you call a cylinder what some texts call a shell?
 
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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