Q6) (10 pts.) Find the area of the region R enclosed by $y = x^2$ and the line $y = Tx + T + 1$.
(i) Express as a double integral in the order of $dydx$
(ii) Express as a double integral in the order of $dxdy$
(iii) Calculate the area.
Q7) (10 pts.) Consider the region between $y = T$, $y = 2T$, $x = 0$ and $y = ln x$. Express the area of R
as a double integral:
(i) in the order of integrations $dxdy$
(ii) in the order of integrations $dydx$.