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Math Help - improper integrals

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    improper integrals

    \int e^{2x}dx [-infinity,0]

    I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= \frac{e^{2x}}{2} . I got (1/2)-0 = 1/2. Did I do this right??
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    Quote Originally Posted by saiyanmx89 View Post
    \int e^{2x}dx [-infinity,0]

    I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= \frac{e^{2x}}{2} . I got (1/2)-0 = 1/2. Did I do this right??
    Correct.
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  3. #3
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    Quote Originally Posted by saiyanmx89 View Post
    \int e^{2x}dx [-infinity,0]

    I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= \frac{e^{2x}}{2} . I got (1/2)-0 = 1/2. Did I do this right??
    \lim_{a \to -\infty} \int_a^0 e^{2x} \, dx

    \lim_{a \to -\infty} \left[\frac{1}{2}e^{2x}\right]_a^0

    \lim_{a \to -\infty} \left[\frac{1}{2} - \frac{1}{2}e^{2a}\right] = \frac{1}{2}
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