4.4-4.5 Test Flashcards
(14 cards)
How do you find the exact value of a definite integral using the Fundamental Theorem?
You should find the antiderivative of the function, then plug in the largest value into the antiderivative and then plug in the smaller value and subtract that from the largest.
If you are shown a picture and asked to find the area of a given region, what do you do?
You should find the antiderivative of the function, then plug in the largest value into the antiderivative and then plug in the smaller value and subtract that from the largest.
If you are given an equation but no x-values but asked to find the area of a given region, what do you do?
You likely know the domain, so just find the zeroes of the function before finding the antiderivative and use those values
How do you find the average value of a function on a closed interval?
Do 1 over b-a times the antiderivative of the function then plug in the domain values and subtract them.
How do you find the net change of a function?
You will know one of the values so subtract or add that to this: the antiderivative of the function, then plug in the largest value into the antiderivative and then plug in the smaller value and subtract that from the largest.
If a function is continuous what else do we know about it?
It is integrable, you can find an antiderivative
How do you find the antiderivative of an absolute value?
Find the value where a is greater than 0 and when it is negative. Then, the negative one, put a negative sign in front of it and make that indefinite integral with its domain and do the same for the positive one. Then find the antiderivative of the function, then plug in the largest value into the antiderivative and then plug in the smaller value and subtract that from the largest. And add the two together.
If you are given a graph of an antiderivative how do you know when the original function is increasing or decreasing?
The graph of the antiderivative is f’ for example, so f is increasing when f’ is positive and the opposite when f’ is negative.
Second Fundamental Theorem
When you have a definite integral going to another variable, do the normal stuff(find the antiderivative of the function, then plug in the largest value into the antiderivative and then plug in the smaller value and subtract that from the largest) except also multiply by the derivative of what you plugged in
Displacement
How far the object moved from its starting position
How do you find displacement?
indefinite integral from a to b of v(t)dt
How do you find total distance traveled?
indefinite integral from a to b of absolute value of v(t)(speed) dt
Point of inflection
When the concavity changes, meaning the second derivative
How do you find relative extrema?
It is when f’(x)=0
