Area Under Curve

Front

What is the formula for calculating the area under a curve represented by a function f(x) from a to b?

Back

Front

Define the term 'definite integral'.

Back

A definite integral is an integral that has specified upper and lower limits, representing the net area under the curve of a function between those limits.

Front

What does the area under a curve represent in a real-world context?

Back

The area under a curve can represent various quantities, such as total distance traveled over time, total revenue over a period, or total accumulated value.

Front

How do you find the area between two curves, f(x) and g(x)?

Back

Front

What is the significance of the Fundamental Theorem of Calculus?

Back

Front

Calculate the area under the curve y = 8 - 2x - x^2 from x = -2 to x = 2.

Back

Front

What is the area under the curve y = 2x from x = 0 to x = 4?

Back

Front

Find the area under the curve y = x^2 from x = 1 to x = 3.

Back

Front

What is the area under the curve y = 3 from x = 0 to x = 5?

Back

Front

Define 'antiderivative'.

Back

An antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).