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Summary Area Between Curves | Calculus II Notes CA$11.51
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Summary Area Between Curves | Calculus II Notes
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Provides a concise description of how to solve the area between curves using integration. Includes examples and step-by-step instructions.

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  • July 20, 2023
  • 2
  • 2022/2023
  • Summary

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1.5 Area Between Curves
There are two types of areas between curves:




Type(I) Type(I) x y(y)
=




fe S"
f(x)
-n
=




- g(x)
=




=
x ax b
=




Type I:
xx*


->
y g(x)
=
f(xx)

= ~
g(Xk*)
=
x ax b
=



X1 &k



before, divide equal parts of width the kit sub interval
as
[Xx 1,Xx]
Ca, b1
into n AX=
9 on

-




Choose X,* and estimate the area of the strip by the area of the rectangle height
of

f(x,*) -




g(Xx*)
Ak [f(xx*)
=
-



g(Xx*))AK
add all areas and take the limitas n =
x




A
=

4..; (f(x*)-g(x,*)IAX Sa(fIX) -g(x)Idx
=




limit of a Reimann sum




SteDS:
1) Sketch the graphs and identify the region
2) draw a typical'rectangle
3)constructthe integral (s)



eg. Ofind the area bounded by y ex and
y
x2-1 on [-1,27
=
=




exy xa-




I
=




i- typical scie




A S_[ex- (x2-1)]dx
=




:J.Sex x +11dx -




2

ex
x x
=
- +




10 +
=2
2 1 1)
+

-

2
+ - -




1
=er--

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