IXL - Evaluate definite integrals using graphs (Calculus practice)

Evaluate the integral

∫

–

You can use the graph of

(

)

to help.

Write an exact, simplified answer.

∫

–

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Learn with an example

question

Evaluate the integral

∫

You can use the graph of

(

)

to help.

Write an exact, simplified answer.

∫

key idea

(

)

is integrable, then the integral

∫

(

)

is equal to the net area between the graph of

(

)

and the

-axis

from

That is, it 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 region between the graph and the

-axis

from

is a trapezoid above the

-axis.

The trapezoid has vertical bases of lengths 3 and 5 and a horizontal altitude of 4. There are no regions below the

-axis,

so the integral is equal to the area of this trapezoid.

∫

(

Area above the x-axis

)

–

(

Area below the x-axis

)

(

)

–

(

)

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Work it out

Not feeling ready yet? These can help:

Q.4Definite integrals and net area

U.6Graph circles

H.3Graph an absolute value function

D.2Graph a linear function

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