Unit 4 Flashcards
Area of a trapezoid formula
(B1 + b2/ 2)*h
What happens to middle bases in a trapezoid integral
All the middle bases are repeated twice
When is the substitution used
Where chain rule would be used so on a composite function
What is odd times even function
An odd function
Is sin odd or even
Sin odd
Is cosine odd or even
Cosine even
Is tangent odd or even
Tangent is odd
When explaining the meaning of an integral what unit will it be in
it will always be in a distance unit like meters or feet not a time unit like seconds or minutes
if m”(t)>0 [m”(t) greater than 0]would it be an over or underestimate
underestimate
an overestimate is
m”(t)<0
m”(t) less than 0
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
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)
When doing left and right Riemann sums and you have to plug into a function what do you do
you plug in The rest of the bases but you don’t plug in the first base
midpoint Riemann sum
Just multiply midpoint by height of a rectangle
when doing a trapezoidal sum with a table do what?
do it every two columns for the trapezoid not just every other or it’s a rectangle
For midpoint Riemann sum
multiply the height or the Y axis by the total width of each individual rectangle
estimate average value
1/b-a multiplied by the area underneath(the integration)
Estimate using Left endput and right endput is the same as
using left and right Riemann sum
e^2x dx =
1/2 e^2x + C
1/x dx
ln |x| + C
3x^2/x^3-5
ln |x^2-5| + C
-sin x/ cos x dx
ln |cos x| + C
when do you use natural log on integration
when the top is the derivative of the bottom
when to use 2nd fundamental thrm of calc
when bottom limit is a number and the top limit is a variable or constant
how to use 2nd fundamental thrm of calc
plug in upper limit(constant(x) )into function then find derivative of upper limit (constant(x))
(x^2)^3
x^6
average value of [-1,3] is
1/b-a
1/3 - -1 times the integration of f(x)
when the integral is from -4 to 4 and the function is even di what
multiply the integral by 2 and set ut from 0 to 4 cuz it is reflective across the y axis
integral of an odd fucktion is wjat
0
integration inches per hour
inches
average value inches per hour
inches oer hour
derivative inches per hour
inches per hour squared
average value of veñocity wirh velocity formula
avergae value 1/b-a times integral
avergae acceñerstion witj velocity function
fo rate of change with velocity function
v(b)-v(a)/b-a
to determike the change in position integrate what?
velocity
find totsl distance travled of particle
use regular inegration with intervals and do absolute value of v(t)
to estimate the accelrstion of the vehicle when given veñoctiy claues do what
find average rate of change close to that time
what do you need to determine the vaergae value of velocity
the position function or the velocity function so you can integrate and find position
when you see a fraction with a 1 on top ok front of the integral what may that orepresent
average value function if it aligns with the intervals
area of quarter circl
pi(r)/ 4
when finding are of circle use what for r
radius half of diameter!!
f(6)-f(4) equals wayt using integrstion
ibtegral of f’(x) from [4,6]
the deriavtive in fornt do the integral does what
cancels out the integral so its. aregular function
if there is an ednpoint at f(b) csn u find the derisvtive
no it DNE
