Properties of Definite Integrals

Front

What is a definite integral?

Back

Front

What is the Fundamental Theorem of Calculus?

Back

Front

How do you calculate the area under a curve using definite integrals?

Back

Front

What is the relationship between definite integrals and the area of regions?

Back

Definite integrals can be used to find the area of regions bounded by the curve, the x-axis, and vertical lines at x=a and x=b. The integral gives the net area, accounting for areas below the x-axis as negative.

Front

Back

Front

What is the property of additivity in definite integrals?

Back

Front

How does the definite integral behave under a change of limits?

Back

Front

What is the significance of the area under the curve in real-world applications?

Back

The area under the curve can represent various real-world quantities, such as total distance traveled, total accumulated quantity, or total profit over time, depending on the context of the function.

Front

What is the relationship between definite integrals and average value of a function?

Back

Front

What is the geometric interpretation of a definite integral?

Back

Geometrically, a definite integral represents the net area between the curve of the function and the x-axis over a specified interval.