Given that $\frac{dy}{dx}=4x+7$dydx=4x+7, consider the following.
Find an equation for $y$y.
Use $C$C as the constant of integration.
Solve for $C$C if the curve passes through the point $\left(3,41\right)$(3,41).
Hence find the equation of $y$y.
Suppose $\frac{dy}{dx}=9x^2-10x+2$dydx=9x2−10x+2.
Find the equation of $y$y in terms of $x$x given that $\frac{dy}{dx}=12\left(x-1\right)^3$dydx=12(x−1)3 and $y=247$y=247 when $x=-2$x=−2.
You may use $C$C as the constant of integration if necessary.
Find the equation of a curve given that the gradient at any point $\left(x,y\right)$(x,y) is given by $\frac{dy}{dx}=\left(x-6\right)^2$dydx=(x−6)2, and that the point $\left(3,-4\right)$(3,−4) lies on the curve.
Use $C$C as the constant of integration.