Originally Posted by

**sparky** Hi,

I'm I on the right track with this problem? Thanks in advance!

**1. The problem statement, all variables and given/known data**

Evaluate the definite Integral, if it exists

**2. Relevant equations**

integral (lower limit = 0, upper limit = square root of pi) of x cos (x^2) dx

**3. The attempt at a solution**

integral (lower limit = 0, upper limit = square root of pi) of x cos (x^2) dx

Let U = x^2

du/dx = 2x

du = 2xdx

dx = du / 2x

integral (lower limit = 0, upper limit = square root of pi) x cos u du/2x = (1/2) cosu du.

Integrating this gives (1/2) sin(u). Nou substitute u=x^2 and solve (1/2)sin(x^2) for the upper and lower limits.

(x/2 * - sin u 1/2x) + C

-1/4 [ sin u ] + c

-1/4 [ sin x^2 ]

-1/4 [ sin pi ] - [ 1/4 sin 0 ]

= 0