Ch 7 Test Review Areas and Volumes

Front

What is the formula to find the area between two curves?

Back

Front

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis from x = 0 to x = π about the x-axis?

Back

Front

How do you determine the volume of a region bounded by two curves rotated about a line?

Back

Front

What integral would find the area of the region enclosed by the curves y = -\frac{x^2}{2} + 4x - 3 and y = -x^2 + 6x - 8?

Back

Front

What is 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

Front

What is the formula for the volume of a solid of revolution using the disk method?

Back

Front

What is the formula for the volume of a solid of revolution using the shell method?

Back

Front

What is the significance of the limits of integration in area and volume problems?

Back

The limits of integration define the interval over which the area or volume is calculated, representing the bounds of the region.

Front

How do you find the area under a curve using integration?

Back

Front

What is the relationship between definite integrals and the area under a curve?

Back

A definite integral calculates the net area between the curve and the x-axis over a specified interval.