The Definite Integral summative

Question 1

Integral Theorem

Answer 1

If fn is continuous on [a,b], then the definite integral exists

Question 2

Integral definition

Answer 2

The integral is the limit of sums of area of partitions as the number of partitions approaches infinity

Question 3

Net area

Answer 3

(a+c) - b

Question 4

Total area

Answer 4

a + c + b

Question 5

Average value of a fn

Answer 5

1/(b-a) times the integral

Question 6

MVT for definite integrals

Answer 6

There is a number c such that a rectangle with base [a,b] and height f(c) has the same area as the region under the graph from a to b

Question 7

FTC part 1

Answer 7

If the fn is continuous on [a,b], the derivative of a definite interval is the fn. evaluated at its upper limit

Question 8

FTC part 2

Answer 8

If the fn is continuous on [a,b] and F is any antiderivative of f on [a,b], then the integral is the difference between the antiderivative of the upper and lower bounds

Question 9

FTC 1 gives

Answer 9

an equation

Question 10

FTC 2 gives

Answer 10

a value

Question 11

Definition of trapezoidal approximation

Answer 11

(b-a)/h [y1 +2y2 +2y3 … + 2y(n-1) + yn]