A solid right (noncircular) cylinder has its base R in the xy-plane and is bounded above by the paraboloid zequalsx2plusy2. Th
e cylinder's volume is VequalsIntegral from 0 to 1 Integral from 0 to y (x squared plus y squared )dx dyplusIntegral from 1 to 2 Integral from 0 to 2 minus y (x squared plus y squared )dx dy Sketch the base of the region R and express the cylinder's volume as a single iterated integral with the order of integration reversed. Then evaluate the integral to find the volume.
1 answer:
Answer:
a. V = 4/3
b. See attachment
Step-by-step explanation:
a.
Given
Z = x² + y²
V = ∫ ∫ (x² + y²) dxdy {0,1}{0,y} + ∫ ∫ (x² + y²) dxdy {0,1}{x,2-x}
V = ∫ ∫ (x² + y²) dxdy {0,1}{x,2-x}
Integrate with respect to y
V = ∫ x²y+ y³/3 dx {0,1}{x,2-x}
V = ∫ x²(2-x) + (2-x)³/3 - x²(2) - (2)³/3 dx {0,1}
V = ∫ 2x² -7x³/3 + (2-x)³/3 dx {0,1}
V = 2x³/3 - 7x⁴/12 + (2-x)⁴/12 {0,1}
V = (⅔ - 7/4 + 2/12) - (0-0+16/12)
V = 4/3
You might be interested in
Answer:
We can predict the sales representative travelled 8 miles replacing x =8 and we got:
And we can predict the sales representative travelled 11 miles replacing x =11 and we got:
Step-by-step explanation:
For this case we have the following data:
Miles Traveled x: 2,3,10,7,8,15,3,1,11
Sales y :31,33,78,62,65,61,48,55,120
For this case we need to calculate the slope with the following formula:
Where:
So we can find the sums like this:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
We can predict the sales representative travelled 8 miles replacing x =8 and we got:
And we can predict the sales representative travelled 11 miles replacing x =11 and we got:
Step-by-step explanation:
Below is an attachment containing the solution
