Question

If dy/dx=xcosx^2 and y=-3 when x=0, when x=pi, y=___.

-3.215
sqrt2
1.647
6
3pi

Answer 1

dy = x cos(x^2) dx
letting u = x^2, we have dy = 1/2 cosu du, so
y = 1/2 sin(x^2) + c
y(0) = -3, so c = -3 and thus
y(x) = 1/2 sin(x^2) - 3
y(π) = 1/2 sin(π^2) - 3 ≈ -2.9
I suspect a typo somewhere ...