The Definite Integral - Weebly

[Pages:22]The Definite Integral

Day 6 Motion Problems Strategies for Finding Total Area

ARRIVAL---HW Questions

Working in PODS

Additional Practice--Packet p. 13 and 14

?Make good use of your time! ?Practice makes perfect! ?Ask ME questions, ask your

CLASSMATES questions!

Area Problems

Review Problem ......

1. Set up an integral that represents the shaded region. 2. Evaluate the integral using the Fundamental Theorem of

Calculus THEN confirm your answer with " fnInt"

f (x) = x2

? 3 x2 dx = 9 0

Find the area of the shaded region

f (x) = x2

Discuss with your partner what we need to do to find the area of the shaded region.

Important to Remember: Integrals find area between the curve

and the x-axis.

27 - 9 = 18

Remember .....

? When evaluating integrals, "areas" beneath the x-axis are negative. ? When evaluating total area, all areas are positive.

a) Evaluate the integral 12

f (x)dx

0

f(x)

12

4

12

f (x)dx f (x)dx f (x)dx 3 7 4

0

0

4

4

12

a) Find the total area of the graph

12

4

12

f (x)dx f (x)dx f (x)dx

0

0

4

3 7 10

Practice--Find the area of the shaded region. NO CALCULATOR

YOU TRY!!

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