Unit 8 TEST

Front

What is the DISC method in calculus?

Back

The DISC method is a technique used to analyze the volume of solids of revolution by breaking down the solid into differential elements and integrating.

Front

How do you find the area between two curves?

Back

To find the area between two curves, integrate the difference of the functions over the interval where they intersect.

Front

What is the formula for the area of the region bounded by the curves y = f(x) and y = g(x)?

Back

Area = \int_{a}^{b} (f(x) - g(x)) \, dx, where a and b are the points of intersection.

Front

What does the Average Value of a function represent?

Back

The Average Value of a function f on the interval [a, b] is given by \frac{1}{b-a} \int_{a}^{b} f(x) \, dx.

Front

How is acceleration related to velocity in calculus?

Back

Acceleration a(t) is the derivative of the velocity function v(t), expressed as a(t) = \frac{d}{dt} v(t).

Front

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

Back

Volume = \pi \int_{a}^{b} [f(x)]^2 \, dx, where f(x) is the function being revolved.

Front

What is the significance of the points of intersection of two curves?

Back

The points of intersection are the limits of integration when calculating the area between the curves.

Front

How do you determine the volume of a solid rotated about a line?

Back

Use the washer method or shell method, depending on the axis of rotation and the functions involved.

Front

What is the relationship between instantaneous rate of change and derivatives?

Back

The instantaneous rate of change of a function at a point is given by the derivative of the function at that point.

Front

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

Back

Volume = 2\pi \int_{a}^{b} (radius)(height) \, dx, where radius and height are defined based on the axis of rotation.