Question

how do you find the limits of a double integral if they give you y = x^2 and y = 2x ?

Answer 1

solve the system of equations \(y=x^2\) and \(y=2x\)
these values will be your \(x_L\) and \(x_R\)

\(y_B=x^2, y_T=2x\)
\[\Large \iint_R f(x,y) \mathrm dA=\int_{x_L}^{x_R} \int_{y_B}^{y_T} f(x,y) \mathrm dy \mathrm dx\]

Answer 2

would the limits of x be 0,2 and y would be from x^2 to 2x ??