Question

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

Answer 1

first we are going to do this by substitution methos let u=x^2 and du=2xdx and (1/2)du=xdx

and now we have (1/2)cosu du to integrate that we get (1/2)sinu +c = y and now sub our u back in to get y = 1/2(sinx^2) +c

Answer 2

Or use the sub method as @hamza_b23 said.

Answer 3

and now to find c we are given that y=-3 x=0 so now we got -3 = c and now let us plug this in to get y = 1/2(sinx^2) - 3

and now finally plug x=pi in to get c yes you are right

Answer 4

i am getting -2.823 but that looks like the closest value i guess