## anonymous 3 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!

1. anonymous

The correct equation I'm referring to is: $\int\limits_{}^{} 9.8e^(0.196t) dt = 50e^(0.196t);$

2. anonymous

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.