Chapter 5 (intro to integration)

Question 1

delta x [a,b]

Answer 1

(b-a)/n

Question 2

xk

Answer 2

k is any number, Xk= a+k(delta x)

Question 3

what are the types of rhiemans sums

Answer 3

left (when Xk* is the left limit of the rectangle)
right (when Xk* is the right limit of the rectangle)
middle (when Xk* is the middle limit of the rectangle)

Question 4

sigma c (c=real number)

Answer 4

cn

Question 5

sigma k

Answer 5

(n(n=1))/2

Question 6

sigma k^2

Answer 6

(n(n+1)(2n+1))/6

Question 7

sigma K^3

Answer 7

(n^2(n+1)^2)/4

Question 8

xk* left rhiemans sum

Answer 8

a+(k-1)delta x

Question 9

xk* right rhiemans sum

Answer 9

a+k(delta x)

Question 10

xk* mid rhiemans sum

Answer 10

a+(k-.5)(delta x)

Question 11

what is xk*

Answer 11

a point in the Kth interval

Question 12

reverse

Answer 12

int(a-b) fxdx =-int(b-a) fxdx

Question 13

general summation rhiemans sum

Answer 13

sigma f(Xk*)(delta x)

Question 14

steps for evaluating an integral with Riemann sums

Answer 14

1. writhe the general equation
2. find delta x
3. find Xk* using the type of limit you want
4. plug in to get one summation equation
5. Use summation notation to replace all of the k’s and numbers with n (hint (Xk*)&(delta x) will have parts that pull through)
6. simplify the equations until you can take the limit as the system approaches infinity.

Question 15

area with the fundamental theorem of calculus.

Answer 15

just take the integral and evaluate at the top bound and subtract eh evaluation at the bottom bound.

Question 16

what trig functions are even

Answer 16

cos x and sec x

Question 17

what trig functions are odd

Answer 17

everything but cos x and sec x

Question 18

average value of a function

Answer 18

Af=(1/b-a)*(int a to b) f(x)

Question 19

mean value theorem for integrals.

Answer 19

if a function is continuous and integratable on the interval a to b then there exist a point on the interval a to b that is equal to the average of the integral from the average value theorem

Question 20

how to integrate by substitutiom

Answer 20

identify the inside and the outside function
inside function is u
derive u and factor it out of the original function. replace with du
then integrate
plug u back in and go on your merry way