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MoonlitFate

  • 3 years ago

Use the Fundamental Theorem of Calculus to determine the answer to the problem; do not use the even/odd properties of integration.

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  1. mathsucks45
    • 3 years ago
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    56665

  2. MoonlitFate
    • 3 years ago
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    Problem is: \[\int\limits_{-\frac{ \pi }{ 2 }}^{\frac{ \pi }{ 2 }}(\sin^3x \cos x+\sin x \cos x)dx\]

  3. phuchh1402
    • 3 years ago
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    \[\sin ^{2} x is meant (\sin(x))^{2}\] so you are using quotient rule for sin square. and cos x anti-derivative was sin x

  4. phuchh1402
    • 3 years ago
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    Then plug pi/2 and - pi/2 in the equation

  5. phuchh1402
    • 3 years ago
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    Then take the number when you plug pi/2 subtract the number when you plug -pi/2 and get the answer

  6. phuchh1402
    • 3 years ago
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    Hope this help

  7. stamp
    • 3 years ago
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    @MoonlitFate find the integral using u substitution (see attachment)

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  8. stamp
    • 3 years ago
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    then evaluate the integral from b to a (see attachment 2) verification of answer @ http://www.wolframalpha.com/input/?i=integral+of+sin^3xcosx%2Bsinxcosx+from+-pi%2F2+to+pi%2F2

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