The document discusses calculating the area under a curve using numerical and algebraic methods. The numerical method involves slicing the region into strips and adding the areas, taking the limit as the width approaches zero. This is the definition of a definite integral. Algebraically, the exact area can be found by integrating the function defining the curve between the bounds.

1. Area
Curves
Between
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2. Review:
1. a. State the numerical methods used to calculate the approximate value of the definite integral:
b. State the algebraic method used to calculate the exact value of the definite integral.
Calculus provides a way to find the exact area under
a curve by slicing a region into strips, adding the
strips together and then taking the limit.
(x, y)
b dA = y dx
Area = ∫dA
a Length
is
constant
dx
a b
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3. 1. Find points of intersection.
2. Slice region into vertical strips of width dx.
3. Show a representative strip and a sample point.
4. Write a differential (dA) representing the area of the strip.
5. Add up all the strips and take the limit as dx approaches 0.
(In other words, integrate.)
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4. Method 1: Subtract areas (Gus' method):
Method 1: Integrate with respect to x: Method 1: Integrate with respect to y:
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