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!

Question

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!

anonymous · Answer

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

anonymous · Answer

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.