Fundamental Theorem of Calculus

[Hckyplayer8]

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.

 

[Steven G]

Do you see clearly that the C's will always cancel out? If you do, then stop writing the Cs.

 

[Hckyplayer8]

Do you see clearly that the C's will always cancel out? If you do, then stop writing the Cs.

Will do. What was the point of adding the constants in the first place?

 

[Steven G]

Note that if \(\displaystyle \int f(x) dx = F(x) + C\),
then \(\displaystyle \int_{a}^{b} f(x) dx = (F(x) + C)\Big|_a^b = (F(b) + C) - (F(a)+C) = F(b) - F(a)\)

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