### From the Calculus Homework

**Question:**State the Fundamental Theorem of Calculus in your own words.

**Selected Answers:**

- The Fundamental Theorem of Calculus was named in very good corrilation [sic] with its purpose. It (FTC) makes a connection with 2 branches of calculus: differential calculus & integral calculus. The FTC gives the precise inverse relationship between the derivative and the integral.
- The area under a curve with a given equation from
*a*to*b*is the antiderivative of that function whereas*F*(*b*) -*F*(*a*) is the area. And if a function is described by*f*(*y*) and is looked at from*a*to*x*, then the antiderivative is*f*(*x*). - The Fundament [sic] Theorem of Calculus relates differential calculus and integral calculus together. Differential calculus deals with tangential equations and integral calculus deals with areas. It may be difficult for one to see how these two branches of calculus relate to each other. The best way to understand how they are connected is when given the equation of a line. If one was to evaluate the integral of the equation from
*a*to*b*one would find that it would equal the area under the graph of the line from*a*to*b*. Thus, correlating integral calculus to differential calculus. - Fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. This means that if a continuous function is first integrated and then differentiated, the original function is retrieved.

That last one seems to have missed the "in your own words" part.