Let y=y(x) solve dydx=2(x+1).

Question

Let $y=y(x)$ solve $\dfrac{dy}{dx}=2(x+1)$. If the area bounded by $y=y(x)$ and the $x$-axis is $\dfrac{4\sqrt8}{3}$, find $y(1)$.

Answer: 2

Accepted Answer

$y=x^2+2x+C$. Setting up the area condition between the roots of $y=0$ and solving the resulting cubic in $C$ gives $C=-1$, so $y=x^2+2x-1$, giving $y(1)=1+2-1=2$.

Solutions · 1