Question

Derive Integral equation for dy/dv

Answer 1

By the fundamental theorem of calculus,

`\displaystyle y = \int_0^v √(3+4t^2) \, dt \implies \boxed{(dy)/(dv) = √(3+4v^2)}`

In general,

`\displaystyle (d)/(dx) \int_0^(g(x)) f(u) \, du = f(g(x)) (dg)/(dx)`