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watch out for goombas
watch out for goombas asked in Science & MathematicsMathematics · 7 years ago

How do i find the anti-derivative of cos2x?

i have looked up the answer and you get it by using u substitution.. however I'm really really confused!!! could someone please walk me though it. 1 specific pont im confused about is how you magically get 1/2 multiplied by cos(u) du. where did that 1/2 come from?

4 Answers

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  • Sky - Vhin
    Lv 6
    7 years ago

    integral of (cos2x)dx

    u = 2x

    du = 2dx

    integral of 1/2(cos2x 2dx)

    =1/2 sin2x + C

    du = 2dx (did you notice the 2?)

    That's why 1/2 was multiplied, because 2*(1/2) = 1.

  • ?
    Lv 7
    7 years ago

    Well,

    this is not so difficult,

    as we have

    (sin(2x) ) ' = 2 cos(2x)

    we ust need to "compenssate" the factor 2,

    therefore :

    the primitive is :

    F(x) = (1/2)sin(x) + Constant

    hope it' ll help !!

  • cidyah
    Lv 7
    7 years ago

    ∫ cos 2x dx

    Let u= 2x

    du = 2 dx

    dx = (1/2) du

    ∫ cos 2x dx = (1/2) ∫ cos u du

    = (1/2) sin u

    = (1/2) sin 2x + C

  • JOS J
    Lv 7
    7 years ago

    the anti-derivative of Cos[a x]

    is

    Sin[a x]/a

    Let a = 2

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