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Area Between Two Curves

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How do you find the area between two curves?. Area Between Two Curves. What is the area underneath the curve of from to ?. What is the area underneath the curve of from to ?. What is the area between the curves of and from to ?. Area between two curves:. When . - PowerPoint PPT Presentation
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Area Between Two Curves How do you find the area between two curves?
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Page 1: Area Between Two Curves

Area Between Two CurvesHow do you find the area between two curves?

Page 2: Area Between Two Curves

What is the area underneath the curve of from to ?

∫0

4

(5𝑥−𝑥2)𝑑𝑥 ¿ [ 52 𝑥2− 13 𝑥3]04

¿18 23

What is the area underneath the curve of

from to ?∫0

4

𝑥 𝑑𝑥 ¿ [ 12 𝑥2]04

¿8

What is the area between the curves of and from to ?

∫0

4

(5𝑥−𝑥2)𝑑𝑥−∫0

4

𝑥 𝑑𝑥¿18 23−10=823∫

0

4

(5𝑥−𝑥2−𝑥 )𝑑𝑥∫0

4

(4 𝑥−𝑥2)𝑑𝑥

Page 3: Area Between Two Curves

− ¿¿

Page 4: Area Between Two Curves

Area between two curves:

When

𝑨=∫𝒂

𝒃

[ 𝒇 (𝒙 )−𝒈 (𝒙 ) ]𝒅𝒙

Page 5: Area Between Two Curves

Example 1Find area of the region bounded by the graphs of and between and .

¿∫0

1

(𝑥2+𝑥+2 )𝑑𝑥

Page 6: Area Between Two Curves

Find area between and .

Since between

Find where the graphs intersect.

Example 2: Region between two intersecting graphs.

− (𝑥2+𝑥−2 )=0

Page 7: Area Between Two Curves
Page 8: Area Between Two Curves

If curves intersect at more than one point.

Page 9: Area Between Two Curves
Page 10: Area Between Two Curves

Horizontal Area• Sometimes it will be more convenient to find

the area of a region by differentiating with respect to y instead of x.

Page 11: Area Between Two Curves

-Setup your integral from bottom to top and use the y values instead of the x values.

-You will integrate (right function – left function).

∫−2

1

Page 12: Area Between Two Curves
Page 13: Area Between Two Curves

Integrate this same function using .You must divide the integral into two parts.

Page 14: Area Between Two Curves
Page 15: Area Between Two Curves

Summary

1. Non-Intersecting Graphs

2. Intersecting Graphs

3. Graphs with Multiple Intersections

4. Finding Area Horizontally

Page 16: Area Between Two Curves

Homework

Area Between Curves Section 7.1

(1-23 odd, 27, 29) (omit 11)

*For 13-21 odd, set up on paper but you may use your calculator to integrate.*

Page 17: Area Between Two Curves

DELETED SLIDES

Page 18: Area Between Two Curves

Example 2: Region between two intersecting graphs.

Find area between and .

Find the points where graphs intersect and integrate from the x

value of the left intersection to the x

value of the right intersection.


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