Question

How can I look at an integral and know whether to use FTC or U-substitution?

Answer 1

Do you mean FTC, Part 1?\[\Large\rm \frac{d}{dx}\int\limits_0^x f(t)dt=f(x)\]This one?

Answer 2

Part one and two.

Answer 3

You're always applying part two when you have `bounds on your integral`.
You're apply the FTC, Part 1, when you're taking a derivative of an integral.

Answer 4

I'm nooooooot exactly sure how that relates to U-substitution though hehe

Answer 5

The thing is, I'm getting questions that ask me to evaluate the integral, so I'm not always sure which method to use because I think it includes u-substitution, right?

Answer 6

You use a u-substitution to make your integral easier to solve, therefore you can use Part 2 of FTC.

Answer 7

One is a theorem of integration - FTC , and one is a method of integration - u-substitution.

Answer 8

oh okay!

Answer 9

When you're finding the integral of some function, you're basically finding the area the solid, or even function makes within a certain limit, a certain space. The Fundamental Theorem of Calculus tells you that from a starting point A to an ending point B, you will be integrating so and so function to find area, volume, etc.

Answer 10

thank you both so much!

Answer 11

The FTC holds for all integrals. You will ALWAYS be integrating from the top function, and subtracting the bottom function.

with U-substitution, you're taking a really hard and complex function, and substituting it with a letter so you can use the FTC to evaluate it.

Answer 12

And your welcome :)