Evaluate The Integral: Sin 3x Cos 7x Dx?

Question

Evaluate The Integral: Sin 3x Cos 7x Dx?

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Camila 3 months 2021-11-06T15:25:37+00:00 2 Answers 0 views 0

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    0
    2021-11-06T15:26:57+00:00

    Answer:

    Although we have a product in the integrand, it is not necessary to use integration by parts, you can use the trigonometric identity

    cos(α)sin(β)=12(sin(α−β+sin(α+β)cos⁡(α)sin⁡(β)=12(sin⁡(α−β)+sin⁡(α+β) and use a substitution after that you will find ur answer…

    0
    2021-11-06T15:27:21+00:00

    Answer:

    (cos4x)/8 + C -(cos10x)/10

    Step-by-step explanation:

    We know,

    sin(a+b) = sina.cosb + sinb.cosa

    and, sin(a-b) = sinb.cosa – sinb.cosa

    ∴ sin(a+b) – sin(a-b) =  2sinb.cosa

     = sinb.cosa = 1/2(sin(a+b) + sin(a-b))

    So, sin3x.cos7x = 1/2(sin(7x+3x) – sin(7x-3x))

    = 1/2(sin(10x) – sin(4x))

    ∴ ∫ sin3x.cos7x dx = ∫ 1/2(sin10x – sin4x)

    = -1/2((cos10x)/10 – (cos4x)/4) + C = -(cos10x)/10 + (cos4x)/8 + C

    = (cos4x)/8 – (cos10x)/10 + C

    Hope, you got it:-))

    Please, mark it as brainiest!!

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