M310 L05 15'1 Double Integrals Over Rectangles

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M310 L05 15.1 Double Integrals Over
Rectangles

• Definite Integral of f(x)
• Definite Integral of f(x,y)
• Finding Volumes
• Midpoint Rule
• Average Value of f(x,y)
• Properties of Double Integrals

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15.1 Definite Integral of f(x) and f(x,y)
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15.1 1 Volume under Paraboloid
Estimate the volume of the solid that lies above
the square R 0, 20, 2 below elliptic
paraboloid z 16-x2-2y2 . Divide R into four
squares and choose the sample point to be the
upper right corner of each.
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15.1 2 Integral as a Volume
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15.1 The Midpoint Rule
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15.1 3 Applying the Midpoint Rule
Use the midpoint rule with mn2 to estimate
the integral below.
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15.1 Average Value of a Function
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15.1 4 Average Value of Snowfall
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15.1 Properties of Double Integrals