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Area Between Curves. Objective. To find the area of a region between two curves using integration. Area A of region bounded b y the curves f(x) and g(x) a nd the lines x=a and x=b, w here f and g are c ontinuous and f>g, is .

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Area Between Curves


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Presentation Transcript
objective
Objective

To find the area of a region between two curves using integration

slide3

Area A of region bounded

by the curves f(x) and g(x)

and the lines x=a and x=b,

where f and g are

continuous and f>g, is

example 1
Example 1

Find the area bounded by y = ex and y = x and between the lines x = 0 and x = 1

example 2
Example 2

Find the region bounded by the parabolas and

example 3
Example 3

Find the area bounded by the curves and

example 4
Example 4

Find the area of the region between and

review
Review
  • The area of the region bounded by curves f(x) and g(x), where f > g, between the point a and b, can be represented by the integral?
  • Write the integral that represents the region bounded by f(x) = x2 - 4x and g(x) = -x2 + 2x
  • Calculate the area bounded by the curves f(x) = x + 1 and g(x) = x/2 between x = 0 and x = 4
with trig functions
With Trig Functions

Find the area bounded by curves y = sin x and y = cos x between x = 0 and x = π/2

practice
Practice

Find the area between the curves y = sec2x and y = cos x from x = -π/4 to x = π/4

variations
Variations

Some curves are best treated as functions of y rather than x

Find the area enclosed by y = x – 1 and y2 = 2x + 6.

practice1
Practice

Find the area of the region bounded by the graphs y = x – 1 and y2 = 3 – x

practice2
Practice

Find the area bounded by the curves x = y2 -2 and x = ey and the lines y = 1 and y = -1