Area and Cross Section Volume (Calculus)

Front

What is the formula for finding the area under a curve bounded by the x-axis?

Back

Front

What is the formula for finding the volume of a solid with cross-sections that are semi-circles perpendicular to the x-axis?

Back

Front

What is the formula for finding the area of a region between two curves, f(x) and g(x)?

Back

Front

How do you find the volume of a solid with square cross-sections perpendicular to the x-axis?

Back

Front

Back

Front

What is the formula for the volume of a solid with a base bounded by y = 4 and y = \frac{x^2}{9}, with square cross-sections perpendicular to the x-axis?

Back

Front

What is the definition of a cross-section in calculus?

Back

A cross-section is a slice of a three-dimensional object, taken perpendicular to a specified axis.

Front

What is the significance of the integral in finding area and volume?

Back

The integral sums up infinitesimally small areas or volumes to find the total area or volume.

Front

What does the term 'bounded' mean in the context of area and volume?

Back

'Bounded' refers to the limits or edges that define the region or solid being measured.

Front

What is the relationship between area and volume in calculus?

Back

Area is a two-dimensional measure, while volume is a three-dimensional measure; both can be found using integrals.