Finding Area and Volume (Calc)

Front

What is the formula for finding the volume of a solid of revolution about the y-axis?

Back

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

Front

What is the formula for finding the area between two curves?

Back

The area A between two curves y = f(x) and y = g(x) from x = a to x = b is given by: A = ∫[a to b] (f(x) - g(x)) dx.

Front

How do you find the volume of a solid of revolution about the x-axis?

Back

Use the formula: V = π ∫[a to b] (f(x))^2 dx, where f(x) is the function being revolved.

Front

What is the area under the curve y = f(x) from x = a to x = b?

Back

The area A can be calculated using the integral: A = ∫[a to b] f(x) dx.

Front

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

Back

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

Front

What is the method of disks in volume calculation?

Back

The method of disks involves slicing the solid perpendicular to the axis of rotation, creating circular disks whose volume is summed up.

Front

What is the method of washers in volume calculation?

Back

The method of washers is used when there is a hole in the solid; it involves subtracting the volume of the inner solid from the outer solid.

Front

How do you find the area of the region enclosed by a line and a curve?

Back

Set the equations equal to find intersection points, then integrate the difference between the line and the curve over the interval defined by those points.

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle is given by: A = (1/2) * base * height.

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by: V = πr^2h, where r is the radius and h is the height.