Unit 4

Question 1

Area of a trapezoid formula

Answer 1

(B1 + b2/ 2)*h

Question 2

What happens to middle bases in a trapezoid integral

Answer 2

All the middle bases are repeated twice

Question 3

When is the substitution used

Answer 3

Where chain rule would be used so on a composite function

Question 4

What is odd times even function

Answer 4

An odd function

Question 5

Is sin odd or even

Answer 5

Sin odd

Question 6

Is cosine odd or even

Answer 6

Cosine even

Question 7

Is tangent odd or even

Answer 7

Tangent is odd

Question 8

When explaining the meaning of an integral what unit will it be in

Answer 8

it will always be in a distance unit like meters or feet not a time unit like seconds or minutes

Question 9

if m”(t)>0 [m”(t) greater than 0]would it be an over or underestimate

Answer 9

underestimate

Question 10

an overestimate is

Answer 10

m”(t)<0

m”(t) less than 0

Question 11

Where are is a function of T and the weight of each coin is 3.5 g write an expression for the rate of change in grams per day of the total weight of the coins at T equals 11 days

Answer 11

The rate of change in grams per day of the total weight of the coins at time T equals 11 days is
3.5R’(11)

Question 12

When doing left and right Riemann sums and you have to plug into a function what do you do

Answer 12

you plug in The rest of the bases but you don’t plug in the first base

Question 13

midpoint Riemann sum

Answer 13

Just multiply midpoint by height of a rectangle

Question 14

when doing a trapezoidal sum with a table do what?

Answer 14

do it every two columns for the trapezoid not just every other or it’s a rectangle

Question 15

For midpoint Riemann sum

Answer 15

multiply the height or the Y axis by the total width of each individual rectangle

Question 16

estimate average value

Answer 16

1/b-a multiplied by the area underneath(the integration)

Question 17

Estimate using Left endput and right endput is the same as

Answer 17

using left and right Riemann sum

Question 18

e^2x dx =

Answer 18

1/2 e^2x + C

Question 19

1/x dx

Answer 19

ln |x| + C

Question 20

3x^2/x^3-5

Answer 20

ln |x^2-5| + C

Question 21

-sin x/ cos x dx

Answer 21

ln |cos x| + C

Question 22

when do you use natural log on integration

Answer 22

when the top is the derivative of the bottom

Question 23

when to use 2nd fundamental thrm of calc

Answer 23

when bottom limit is a number and the top limit is a variable or constant

Question 24

how to use 2nd fundamental thrm of calc

Answer 24

plug in upper limit(constant(x) )into function then find derivative of upper limit (constant(x))

Question 25

(x^2)^3

Answer 25

x^6

Question 26

average value of [-1,3] is

Answer 26

1/b-a 1/3 - -1 times the integration of f(x)

Question 27

when the integral is from -4 to 4 and the function is even di what

Answer 27

multiply the integral by 2 and set ut from 0 to 4 cuz it is reflective across the y axis

Question 28

integral of an odd fucktion is wjat

Answer 28

0

Question 29

integration inches per hour

Answer 29

inches

Question 30

average value inches per hour

Answer 30

inches oer hour

Question 31

derivative inches per hour

Answer 31

inches per hour squared

Question 32

average value of veñocity wirh velocity formula

Answer 32

avergae value 1/b-a times integral

Question 33

avergae acceñerstion witj velocity function

Answer 33

fo rate of change with velocity function | v(b)-v(a)/b-a

Question 34

to determike the change in position integrate what?

Answer 34

velocity

Question 35

find totsl distance travled of particle

Answer 35

use regular inegration with intervals and do absolute value of v(t)

Question 36

to estimate the accelrstion of the vehicle when given veñoctiy claues do what

Answer 36

find average rate of change close to that time

Question 37

what do you need to determine the vaergae value of velocity

Answer 37

the position function or the velocity function so you can integrate and find position

Question 38

when you see a fraction with a 1 on top ok front of the integral what may that orepresent

Answer 38

average value function if it aligns with the intervals

Question 39

area of quarter circl

Answer 39

pi(r)/ 4

Question 40

when finding are of circle use what for r

Answer 40

radius half of diameter!!

Question 41

f(6)-f(4) equals wayt using integrstion

Answer 41

ibtegral of f’(x) from [4,6]

Question 42

the deriavtive in fornt do the integral does what

Answer 42

cancels out the integral so its. aregular function

Question 43

if there is an ednpoint at f(b) csn u find the derisvtive

Answer 43

no it DNE