0πecos(x)sin(2x)dx=4e 
 
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0πecos(x)sin(2x)dx=4e     (Decimal:     1.47151)
  • steps
  • 0πecos(x)sin(2x)dx

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    Rewrite using trig identities
    =0πecos(x)· 2cos(x)sin(x)dx

  • Take the constant out:    a·f(x)dx=a·f(x)dx
    =2·0πecos(x)cos(x)sin(x)dx

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    Apply usubstitution:    11euudu
    =2·11euudu

  • abf(x)dx=baf(x)dx, a<b
    =2(11euudu)

  • Take the constant out:    a·f(x)dx=a·f(x)dx
    =2((11euudu))

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    Apply Integration By Parts:    [euu eudu]11
    =2(([euu eudu]11))

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    eudu=eu
    =2(([euueu]11))

  • Simplify
    =2[euueu]11

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    Compute the boundaries:    2e 
    =2·2e 

  • Simplify
    =4e 

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