How do I write an expression for y in terms of x if i'm given dy/dx=cos(x^2) and (1,5)?

Question

I know I can't find the integral of the dy/dx easily so how would i do this?

The integral can't be y = sin(x^2)/(2x) because when finding the derrivative of this equation you use the quotient rule.

Answer 1

This is called a Fresnel function.
You need limits of integration so that you can integrate numerically or a table of the Fresnel function.

Answer 2

hi

suppose dy/dx = (cos x)^2

y = 1/2 ( x + sin x * cos x ) + k

then

k = 5 - (1/2)* ( 1 + sin (1) cos (1))

y = 5 + 1/2 ( (x -1) + (sin x * cos x - sin 1 * cos 1) )

bye