1. ## improper integrals

I have no idea what to do for this problem, could someone please help me and explain how to solve it. thank you!

(a) Sketch the following region. S={(x,y)|x is greater than or equal to -2, 0 less than or equal to y less than or equal to 17e^-x/2}
(b) Find the area of the region

2. Can you at least set up the double integral?

3. Originally Posted by limegreen1545
I have no idea what to do for this problem, could someone please help me and explain how to solve it. thank you!

(a) Sketch the following region. S={(x,y)|x is greater than or equal to -2, 0 less than or equal to y less than or equal to 17e^-x/2}
(b) Find the area of the region
$\lim_{b \to \infty} \int_{-2}^b 17e^{-\frac{x}{2}} \, dx$

$\lim_{b \to \infty} \left[-34e^{-\frac{x}{2}}\right]_{-2}^b$

$-34 \lim_{b \to \infty} \left[e^{-\frac{x}{2}}\right]_{-2}^b$

$-34 \lim_{b \to \infty} \left[e^{-\frac{b}{2}} - e\right]$

$-34\left[0 - e\right] = 34e$