Week 4 - Definite Integrals

Question 1

What is the fundamental theorem of calculus

Answer 1

∫^ba f(x) dx = F(b) - F(a) where F is any antiderivative of f: F’(x) = f(x)

Question 2

Complete the definite integral rule if a and b are switched

Answer 2

∫^ba f(x) dx = - ∫^ab f(x) dx

Question 3

Complete the definite integral rule with a < c < b

Answer 3

∫^ba f(x) dx = ∫^ca f(x) dx + ∫^bc f(x) dx

Question 4

What is the rule if determining the area between to curves?

Answer 4

If f(x) > or equal to g(x) on the interval [a,b], ∫^ba [f(x) - g(x)] dx

Question 5

With indefinite integrals, what would the ∫1/x be?

Answer 5

ln|x| , absolute value is important because it can’t be 0

Question 6

Rewrite ln(x) -ln(y)

Answer 6

ln(x/y)

Question 7

If asked to evaluate an area with two functions, how do you determine which one is above the other?

Answer 7

Plug the boundaries into each function and determine which one has the higher value

Question 8

How do you determine where two curves intersect and if they switch one over the other? 2nd lesson 24:26

Answer 8

Set them equal to each other; solve both equations for a number between each interval and see which is bigger to determine the upper