1. Graph 2. Find the area between the above graph and the x-axis 3. 4. Find the area of each: 7.

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Presentation transcript:

1. Graph 2. Find the area between the above graph and the x-axis Find the area of each: 7

SWBAT: Find the exact area under a curve!

1.Use midpoint Riemann sum with 4 equal subintervals of equal length to approximate the area under the velocity curve of a rocket’s flight. 2.Think about, then discuss what the units might be.

 In general, the sum of all rectangles is:  Where:  Let’s try an example! and

Before this is computed, we need some info:

 If not, review at the end

 Find the area under the curve of y=x 2 on the interval [0,3]

 The process of adding up an infinite number of rectangles with width dx is called...

 In the notation  f(x) is called the integrand  a is the lower limit  b is the upper limit

 Calculate

 Evaluateby interpreting it in terms of area.

 Therefore

 Similarly we can interpret as the difference of areas of two triangles:

 We can define using the following property:  If a = b, then ∆x = 0 and so

 Find your notes:

 Riemann sums with sigma  Definition of definite integral  Interpreting definite integrals as areas

 p.364 #5a,c, 8b  p.366 #33,35,37 56 days ‘til AP exam “When I take it, I will pass!