Chapter 14 Multiple Integrals

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Chapter 14Multiple Integrals
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14.1 Double Integrals
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Recall the Definite Integral
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The Double Integral
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The Iterated Integral
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Fubinis Theorem (First Form)

• If f(x,y) is continuous on the rectangular region
  Ra?x ?b, c ?y ?d, then

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Fubinis Theorem (Stronger Form)

• If f(x,y) is continuous on a region R.
• 1) If R is defined by
• a?x ?b, g1(x) ?y ? g2(x), g1 and g2 continuous on
  a,b, then

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Fubinis Theorem (Stronger Form)

• If f(x,y) is continuous on a region R.
• 1) If R is defined by
• c?y ?d, h1(x) ?x ? h2(x), h1 and h2 continuous on
  c,d, then

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Reversing the Order of Integration