I used mainly deductive reasoning in exploring the fundamental theorem of calculus. Isaac Newton went to hard, though. The fundamental theorem relates derivatives and integrals and makes us able to find the area underneath curves. The uses for this fundamental relationship are astronomical! We can find the distance traveled by objects when we know the acceleration, velocity, or even jerk. We can find the area under weird curves, and find the volume of shapes other than the basic prisms and what not. I keep on being impressed by what these people have figured out. The logic behind these discoveries seem so logical to me but at the same time so clever and world-changing!
So far I've learned that the uses for Calculus are numerous. We use it to calculate orbits of planets, optimize production of goods, optimize volume, make things more efficient, find distance traveled, velocity, and acceleration, find the volume of shapes, and so on. If you can think of a problem then Calculus can probably solve it. (I don't really know that though)
I think that the fundamental theorem of calculus is so fundamental to calculus because understanding this law allows us to use it to solve all of the problems we run into. Without the knowledge of the relationships between integrals, derivatives, and anti-derivatives, then all of this knowledge would just be like a cool little "fun fact" with no uses.
As we continue on through class we keep finding more and more uses for calculus and I'm impressed. I can't wait to find out how the AP test writers are going to try to confuse us with their terminology and wording. Why won't they just let us solve problems and use mathematics without all of these barriers!?
So far I've learned that the uses for Calculus are numerous. We use it to calculate orbits of planets, optimize production of goods, optimize volume, make things more efficient, find distance traveled, velocity, and acceleration, find the volume of shapes, and so on. If you can think of a problem then Calculus can probably solve it. (I don't really know that though)
I think that the fundamental theorem of calculus is so fundamental to calculus because understanding this law allows us to use it to solve all of the problems we run into. Without the knowledge of the relationships between integrals, derivatives, and anti-derivatives, then all of this knowledge would just be like a cool little "fun fact" with no uses.
As we continue on through class we keep finding more and more uses for calculus and I'm impressed. I can't wait to find out how the AP test writers are going to try to confuse us with their terminology and wording. Why won't they just let us solve problems and use mathematics without all of these barriers!?