IXL - Definite integrals and net area (Calculus practice)

This is the graph of

(

)

The areas of the shaded regions are

and

Which expression is equal to

∫

–

(

)

–

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question

This is the graph of

(

)

The areas of the shaded regions are

and

Which expression is equal to

∫

(

)

–

key idea

(

)

is integrable, then the integral

∫

(

)

is equal to the net area between the graph of

(

)

and the

-axis

from

The net area is the area above the

-axis

minus the area below the

-axis.

∫

(

)

(Area above the x-axis)

–

(Area below the x-axis)

solution

The integral

∫

(

)

is equal to the net area between the graph of

(

)

and the

-axis

from

The regions with areas

and

lie within the bounds above the

-axis,

and the region with area

lies within the bounds below the

-axis.

Find the net area.

∫

(

)

(Area above the

-axis)

–

(Area below the

-axis)

(

)

–

(

)

–

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