Area between curves

Front

Define the area between curves.

Back

The area between curves is the region enclosed by two or more curves on a graph. It is calculated using definite integrals.

Front

What is the formula to find the area between two curves, y = f(x) and y = g(x)?

Back

Front

How do you determine the points of intersection of two curves?

Back

To find the points of intersection of two curves, set the equations equal to each other and solve for x. The solutions will give the x-coordinates of the intersection points.

Front

What is the significance of the limits of integration in finding the area between curves?

Back

The limits of integration represent the x-coordinates where the curves intersect, defining the interval over which the area is calculated.

Front

Write the integral to find the area between the curves y = x^2 + 1 and y = 5.

Back

Front

What is the first step in finding the area between the curves x = -3y² + 4 and x = y³?

Back

The first step is to find the points of intersection by setting -3y² + 4 = y³ and solving for y.

Front

Explain how to set up an integral for vertical slices between curves.

Back

Front

What is the area of the region bounded by the curves y = x^2 + 1 and y = 5?

Back

Front

What does it mean if the area between two curves is negative?

Back

A negative area indicates that the lower curve is above the upper curve over the interval considered, which is not physically meaningful for area.

Front

How do you find the area between curves when they are expressed in terms of y?

Back