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Area between curves AP Calculus Mrs. Mongold Gateway Arch, St. Louis, Missouri
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How can we find the area between these two curves? We could split the area into several sections, use subtraction and figure it out, but there is an easier way.
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Consider a very thin vertical strip. The length of the strip is: or Since the width of the strip is a very small change in x, we could call it dx.
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Since the strip is a long thin rectangle, the area of the strip is: If we add all the strips, we get:
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The formula for the area between curves is: We will use this so much, that you won’t need to “memorize” the formula!
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Find the area of the region bounded by:
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If we try vertical strips, we have to integrate in two parts: We can find the same area using a horizontal strip. Since the width of the strip is dy, we find the length of the strip by solving for x in terms of y.
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We can find the same area using a horizontal strip. Since the width of the strip is dy, we find the length of the strip by solving for x in terms of y. length of strip width of strip
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Find the area of the region bounded by:
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Homework Page 380-381/1-10 ALL
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