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Even and Odd SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd
![Even and Odd SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd](http://images.slideplayer.com./32/9926904/slides/slide_1.jpg "Even and Odd SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd")
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Term-102 Even and Odd
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Term-102 Even and Odd
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Term-091 Even and Odd
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Term-102 Even and Odd
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Term-103 Even and Odd
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SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd Example Even and Odd
![SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd Example Even and Odd](http://images.slideplayer.com./32/9926904/slides/slide_7.jpg "SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd Example Even and Odd")
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AREAS BETWEEN CURVES Area between two curves
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AREAS BETWEEN CURVES Area between two curves Find the area of the region bounded by the curves and Example: Both right-hand and left- hand boundary are lines Note:
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AREAS BETWEEN CURVES Area between two curves Both right-hand and left- hand boundary reduce to a point Note:
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AREAS BETWEEN CURVES Area between two curves The value of a and b (not given) Note: Steps: 1) Find the intersection points 2) Write the area as an integral
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AREAS BETWEEN CURVES Area between two curves
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THE SUBSTITUTION RULE T-092
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THE SUBSTITUTION RULE T-102
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AREAS BETWEEN CURVES
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Area between two curves Some regions are best treated by regarding x as a function of y.
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AREAS BETWEEN CURVES Area between two curves Some regions are best treated by regarding x as a function of y.
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AREAS BETWEEN CURVES Steps: 1) Rewrite the function as x in terms of y 2) Find the intersection points
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AREAS BETWEEN CURVES We could have found the area in by integrating with respect to x instead of y, but the calculation is much more involved.
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AREAS BETWEEN CURVES T-092
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AREAS BETWEEN CURVES
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