Fundamental Theorem of Calculus

Hckyplayer8

Full Member
Joined
Jun 9, 2019
Messages
269
1.PNG


Using the Fundamental Theorem of Calculus I found the antiderivative of the integrand. Then I found the difference of the upper and lower bound values inserted into the antiderivative.

I double checked the work both logically with the integral/antiderivative relationship and through symbolab so all should be well. But I wanted to double check and get feedback.
 
Note that if f(x)dx=F(x)+C\displaystyle \int f(x) dx = F(x) + C,
then abf(x)dx=(F(x)+C)ab=(F(b)+C)(F(a)+C)=F(b)F(a)\displaystyle \int_{a}^{b} f(x) dx = (F(x) + C)\Big|_a^b = (F(b) + C) - (F(a)+C) = F(b) - F(a)

The answer to why we have C in the 1st place is for indefinite integral (as my 1st line shows)
 
Top