Posted by **ANONYMOUS** on Wednesday, May 30, 2012 at 8:55am.

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 -
**Damon**, Wednesday, May 30, 2012 at 9:31am
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) -
**Damon**, Wednesday, May 30, 2012 at 10:16am
-.215-3

-3.215

- CALCULUS -
**ANONYMOUS**, Wednesday, May 30, 2012 at 10:34am
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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