Intro to Area Under a Curve

What is an integral?

• A mathematical expression for the area under a curve

• A mathematical expression for the slope of a curve

• A mathematical expression for the distance between two points

• A mathematical expression for the derivative of a function

What is the purpose of an integral?

• To solve for the area under a curve

• To solve for the derivative of a function

• To solve for the distance between two points

• To solve for an unknown function

What is a definite integral?

• mathematical expression for the area between two points

• mathematical expression for the slope of a curve

• mathematical expression for the distance between two points

• mathematical expression for the integral of a function over a given interval

• A
• B
• C
• D

• 40
• 32
• 64
• Not possible

Find the area of the region bounded by the equations y = x² + 1 and y = 5.

• 32/3

• 64

• 32

• 64/3

• 16

• A
• B
• C
• D

CALCULATOR PERMITTED

• A

• B

• C

• D

• E

The shaded area shown in the figure can be represented by which of the following integral expressions?

Find the integral that would find the area of the region enclosed by the curves.