AP Calc: The "Fun"demental Theorem of Calculus

With learning about the fundamental theorem of calculus, I mostly relied on deductive reasoning. I really had no idea what this theorem meant, so I had to rely on the actual facts to understand what it meant. This theorem is very important because it is a basic idea of calculus, although it is very confusing. Once you understand what the theorem means, you have a base for all calculus involving integrals and derivatives. My understanding of this theorem is that when you are finding the derivative of an integral from a number to x, one would need to take the inside function that is inside the integral, and plug in x for the variable. The derivative and the integral cancel eachother out, and the number that the integral starts with becomes zero, since the derivative of a single number is zero. This is why we don’t have to subtract the function with the bottom number from the top because it equals zero. In broad terms, the FTC helps us understand the implications of integrals, derivatives, and antiderivatives.