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 one year ago
Let R be the region in the first quadrant bounded by the graph y=3√x the horizontal line y=1, and the yaxis as shown in the figure to the right.
 one year ago
Let R be the region in the first quadrant bounded by the graph y=3√x the horizontal line y=1, and the yaxis as shown in the figure to the right.

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Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0http://goo.gl/AhgJX Region R is the base of a solid. For each y, where 1≤y≤3, the cross section of the solid taken perpendicular to the yaxis is a rectangle whose height is half the length of its base. Write, but do not evaluate, an integral expression that gives the volume of the solid.

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea how to solve this one, so any and all help is appreciated.

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0How is this supposed to work math wise? I'm having trouble visualizing how that becomes Calc.

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0finally it's back up for me now.

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0... so is that last part there the "actual" answer? I'm trying to wrap my head around your post.

phi
 one year ago
Best ResponseYou've already chosen the best response.1does this make sense each plane is a sheet of volume x*x/2 * dy

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I think so. Thanks.

phi
 one year ago
Best ResponseYou've already chosen the best response.1each plane is a sheet of volume x*x/2 * dy now put everything in terms of all x or all y if we stick with x: y=3√x and \[dy = \frac{1}{2} x^{\frac{1}{2}} \ dx\] the limits of integration will be x=4 to 0 \[ \frac{1}{4} \int_{4}^{0} x^{\frac{3}{2}}\ dx\] or flipping the limits, and negating \[ \frac{1}{4} \int_{0}^{4} x^{\frac{3}{2}}\ dx\] if we go with y: x= (3y)^2 \[ \frac{1}{2} \int_{1}^{3} (3y)^4 \ dy\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1fixed a typo on finding how dy equates to dx. the first way changes dy to a function of x and dx and then integrates over x the second way changes x to a function of y and integrates the volume x^2/2 (in terms of y) over y
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