Calculus

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Evaluate the following integral

integral 1 = a and b = 4 of
sinx dx/(1+cos)^2

u = cosx
du = -sinx dx

so from here I don't know if I can do:

-1 du = sinx dx
or 1/sin du = x dx

  • Calculus -

    u = 1 + cos x
    du = -sin x dx

    so we have
    -du/u

  • Calculus -

    so I tried again and I got this, don't know if it's good:(I also put the wrong a and b)

    integral 0 = a and b = pi/3 of
    sinx dx/(1+cos)^2

    u = cosx
    du= -sinxdx
    -1 du = sinx dx

    so: integral -1 du/(1+u)^2
    = 1/(u+1)

    if x = 0, then u = 1
    if x = pi/3, then u = 1

    so 1/1+1 - 1/1+1 = 0

    Is this correct?

  • I mean -

    -du/(u)^2

  • Calculus -

    -du/u^2 ---> -1/u + c

  • Calculus -

    ok Damon, so if you integrate what you have me, you get 1/u no? Because 1/u^2 = -1/u, so -1/u^2 = 1/u?

  • Calculus -

    so
    -1/(1+cos x) + c

  • Calculus -

    Yes, you have it.

  • Calculus -

    awesome, thanks man!

  • Calculus -

    You are welcome.

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