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

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

phi
 2 years 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
 2 years 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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