CALCULUS

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If dy/dx = x cos x^2 and y = −3 when x = 0, when x = pi, y = .

A. −3.215
B. sqrt(2)
C. 1.647
D. 6
E. 3pi

All of the potential solutions I've come up with don't satisfy any of the given values.

  • CALCULUS -

    dy/dx = x cos x^2
    dy = x cos x^2 dx

    let z = x^2
    dz = 2 x dx so x dx = dz/2
    so we have
    dy = (1/2) cos z dz

    y = (1/2)sin z + c
    when x = 0, z = 0
    -3 = (1/2)(0) + c
    c = -3
    so
    y = (1/2) sin z - 3
    when x = pi, z = pi^2
    y = (1/2) sin(pi^2) - 3
    = -.430-3
    =-3.43 I do not agree either

  • forgot the (1/2) -

    -.215-3
    -3.215

  • CALCULUS -

    Ah-ha! As I was working on this earlier, somehow I got to sin(pi^2) - 3, too. But it gave me the same -3.43. Now that the 1/2 is in there, it makes much more sense.
    Complicated math messes with one's head; you know how to do all the fancy stuff, but then the basic arithmetic flies out the window! lol

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