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stephane02

  • 2 years ago

How the following integral is calculated : \int\limits_{}^{} 9.8e^(0.196t)dt = 50e^(0.196t); I cannot understand the method used here. Th for helping!

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  1. stephane02
    • 2 years ago
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    The correct equation I'm referring to is: \[\int\limits_{}^{} 9.8e^(0.196t) dt = 50e^(0.196t);\]

  2. igortrpevski
    • 2 years ago
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    You can use substitution for the exponent 0.196t = u. Then you calculate dt and du by taking the derivative from both sides of the substitution to obtain 0.196dt = du, and replace dt = du/0.196. The term 9.8/0.196 = 50 just comes out of the integral and you are left with \[50\int\limits e^udu\] which readily evaluates to \[50(e^u+C)\] where C is some integration constant. Then you simply reverse back the substitution u=0.196t.

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