AP Calculus Moving On to Integration

With the start of the new semester came the start of a new topic in AP Calculus, Integrals. Traditionally, calculus courses are split into two parts: differential calculus and integral calculus. Here at Uniontown, our AP Calculus class teaches both halves, and this year’s students just moved on to the latter half. We decided to ask four of the students about their opinions on the new topic.

Cody Lowden

What do you find easy or hard about this new topic?
Training my brain to work backwards form differentiation has been the toughest part so far.
What parts about this new topic do you enjoy or not enjoy?
I enjoy when I see “Integrate e to the x” on exams.
Do you find Integral Calculus to be easier or harder than Differential Calculus? Why?
I personally find it easier because it was just a new leaf for me.
Do you like Integral Calculus more or less than Differential Calculus? Why?
I enjoy Integral Calculus more now because I’m not lost, but I’m sure that will change shortly.
What topic(s) in Calculus have you enjoyed so far?
Sketching derivatives was one of my favorites because I was able to visually see how differentiating altered functions appears.

Madelyn Velosky

What do you find easy or hard about this new topic?
It is based off of previous topics we have learned so I find that is what makes it easier to understand.
What parts about this new topic do you enjoy or not enjoy?
It is like a puzzle and I enjoy working hard to find the answer.
Do you find Integral Calculus to be easier or harder than Differential Calculus? Why?
Easier, because I already had differential as a foundation so it made the transition smoother.
Do you like Integral Calculus more or less than Differential Calculus? Why?
I enjoy Integral Calculus more because it comes easier to me.
What topic(s) in Calculus have you enjoyed so far?
I enjoy integration, derivatives, rectilinear motion, and curve sketching.

Jimmy Thompson

What do you find easy or hard about this new topic?
It is sometimes easy because the problems are noticeably the answer to derivative problems which we have done in the past so some problems can be solved just by using logic.
What parts about this new topic do you enjoy or not enjoy?
I don’t enjoy integral problems that you have to work with before integrating because it’s not very easy to figure out which direction to go.
Do you find Integral Calculus to be easier or harder than Differential Calculus? Why?
Harder because you must have a concrete understanding on Differential Calculus to do Integral Calculus.
Do you like Integral Calculus more or less than Differential Calculus? Why?
I enjoy it less because you can’t always tell which rules you will need for integrals.
What topic(s) in Calculus have you enjoyed so far?
Full curve sketching because it was very systematic with an order of steps to do each time you differentiate leading up to the graphing.

Karsyn Lucy

What do you find easy or hard about this new topic?
I find it easy that it’s new basic problems because we are basically going back to the beginning to learn to do everything again.
What parts about this new topic do you enjoy or not enjoy?
I enjoy the integration because we get to see what we did in previous chapters working backwards.
Do you find Integral Calculus to be easier or harder than Differential Calculus? Why?
I find it easier and harder only because we have focused on Differential Calculus and one way of doing things for so long, so it’s difficult changing my mindset, but I thought doing Differential Calculus was easier to think about.
Do you like Integral Calculus more or less than Differential Calculus? Why?
So far I like Integral Calculus more. We are just starting to get into it, but I like seeing the problems work out.
What topic(s) in Calculus have you enjoyed so far?
I enjoyed learning the rules for differentiation the most, and vice versa, I enjoyed learning the backwards rules for integration.

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