AP Calculus BC Unit 6 Retake

Front

What is the formula for the volume of a solid of revolution when revolving around the y-axis?

Back

The volume V can be calculated using the formula: V = π∫[a to b] (f(x))^2 dx, where f(x) is the function being revolved.

Front

How do you find the volume of the solid generated by revolving the area bounded by y = x^2 and the x-axis from [0, 2] around the y-axis?

Back

Use the formula V = π∫[0 to 2] (x^2)^2 dx = π∫[0 to 2] x^4 dx = π[1/5 * x^5] from 0 to 2 = 8π.

Front

If velocity is negative and increasing, what can be said about the speed?

Back

The speed is decreasing because the object is moving in the negative direction but slowing down.

Front

What integral would allow you to find the volume of the region bounded by y = 2x^2 and y = 8 around the line y = 11?

Back

The integral is V = π∫[0 to 2] [(11 - 2x^2)^2 - 9] dx.

Front

What is the volume of the solid formed by revolving the region bounded by y = x and y = x^2 about the line y = 1?

Back

The volume is V = π/5.

Front

What is the relationship between velocity and speed when velocity is negative?

Back

Speed is the absolute value of velocity; thus, if velocity is negative, speed is positive but decreasing if the velocity is increasing.

Front

How do you set up the integral for finding the volume of a solid of revolution?

Back

Identify the function to be revolved, the axis of rotation, and the limits of integration, then use the appropriate volume formula.

Front

What is the significance of the disk method in calculating volumes of solids of revolution?

Back

The disk method involves slicing the solid into thin disks perpendicular to the axis of rotation and summing their volumes.

Front

What is the washer method in volume calculation?

Back

The washer method is used when there is a hole in the middle of the solid; it calculates the volume of the outer disk minus the inner disk.

Front

How do you determine the limits of integration for volume problems?

Back

The limits of integration are determined by the points where the curves intersect or the specified bounds of the region.