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Math Help - improper integrals

  1. #1
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    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
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  2. #2
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    Can you at least set up the double integral?
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  3. #3
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    Quote Originally Posted by limegreen1545 View Post
    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
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