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emilyoo

  • 2 years ago

simple integration by substitution: 6-5sin(2x)

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  1. emilyoo
    • 2 years ago
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    |dw:1358068473382:dw|

  2. emilyoo
    • 2 years ago
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    this is how far i got

  3. AravindG
    • 2 years ago
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    t=sin x would do it

  4. AravindG
    • 2 years ago
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    because derivative of sinx (ie cos x ) is readily available!

  5. wio
    • 2 years ago
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    you don't even need to use that trig identity by the way.

  6. wio
    • 2 years ago
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    just let \(u=2x\) in the original integral, it'd work fine.

  7. klimenkov
    • 2 years ago
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    \(\int (6-5\cdot2\sin x \cos x)dx=\int6dx-10\int\sin x \cos xdx\). Try to make a substitution \(t=\sin x,\quad dt=\cos x\). Good luck.

  8. AravindG
    • 2 years ago
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    @wio'smethod is the simplest :)

  9. wio
    • 2 years ago
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    \[ \int \sin(2x)dx = \int \sin(u)\frac{ du}{2} \]

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