Hey guys. I'm just looking for some quick math help. These 2 problems are about areas between curves and the volume methods of integration.
1. Find area of region bounded by curves y = x + 5, x = y^2, y = -1, and y = 2.
For #1, I got 16.5.
2. Let R be the region bounded by the x-axis and the curves y = (2+5x^2) ^ (-1/2), x = 1, and x = 4. Find volume obtained by rotating R about y-axis.
For some reason I keep getting a negative answer here. That can't be right for a volume problem. Also, another random note: it does say rotate around y-axis, but even if you did it around x-axis, do you get the same answer?
For #1:
I chose to use horizontal strips, so I converted y = x + 5 into x = y-5.
Thus, I had an interval of -1 to 2, and it was [right curve - left curve] dy. My right curve was y^2, and my left curve was (y-5).
After all the math, I got 16.5. I'm guessing it's incorrect?
For #2, are you just saying to square (2+5x^2) ^ (-1/2) and then take the integral of that? I have to rotate around the y-axis in this problem. I was under the impression that when you rotate around the y axis, you must convert the equation into an x = y equation.
1. The general form of the volume which you get by rotation about the y-axis is:
2. To calculate the volume it isn't necessary to determine x but x²:
If y = f(x) you'll get and
The complete equation to calculate the volume is
3. I've got an approximate value of the volume of 1.07765
4. The volume of rotation at rotation about the x-axis is calculated by:
In genaral the volumes and are unequal.
What region are you talking about? The line y= x+ 5 does NOT intersect the curve between y= -1 and y= 2.
For #1, I got 16.5.
2. Let R be the region bounded by the x-axis and the curves y = (2+5x^2) ^ (-1/2), x = 1, and x = 4. Find volume obtained by rotating R about y-axis.
For some reason I keep getting a negative answer here. That can't be right for a volume problem. Also, another random note: it does say rotate around y-axis, but even if you did it around x-axis, do you get the same answer?[/QUOTE]