Write the standard form of the line that contains a y-intercept of -3 and passes through the point (3, 0). Include your work in
1 answer:
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Explanation:
Let and
. The differential volume dV of the cylindrical shells is given by
Integrating this expression, we get
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
or
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is