Applications of Integration flashcards
40 practice cards drawn from the Applications of Integration lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Applications of Integration lessons in full →
. The displacement from t = 0 to t = 2 is
8
from “Velocity and Displacement by Integration”
v dips below the axis. The signed integral gives
displacement
from “Velocity and Displacement by Integration”
A particle moves off and returns to its start. Its displacement is
0
from “Total Distance Traveled”
The three stretches measure , and . The displacement is
from “Total Distance Traveled”
The limits of that integral come from
where they cross
from “Area Between Two Curves”
To find the area between two curves, integrate
upper minus lower
from “Area Between Two Curves”
Spinning about the y-axis, the integral is
from “Volumes of Revolution”
The volume of revolution integrates
from “Volumes of Revolution”
Compared with the disc method, the washer method needs
the inner disc taken away
from “Volumes by Washers”
y = x and on [0, 1], spun about the x-axis. The volume is
from “Volumes by Washers”
Cross sections are semicircles of diameter s. Each face has area
from “Volumes with Known Cross Sections”
A known-cross-section volume needs
no spinning at all
from “Volumes with Known Cross Sections”
Arc length integrates
from “Arc Length”
The arc length formula comes from
Pythagoras
from “Arc Length”
A function has integral 32 over a width of 4. What is its mean value?
8
from “The Mean Value of a Function”
A function has integral 12 over a width of 4. What is its mean value?
3
from “The Mean Value of a Function”
An infinite region can have a finite area
true
from “Improper Integrals”
An improper integral is defined as
a limit
from “Improper Integrals”
Heights 0, 1, 4 with h = 1. The trapezium estimate is
3
from “Numerical Integration”
The trapezium rule treats each strip top as
a straight slope
from “Numerical Integration”
Simpson’s rule tops each strip pair with a
parabola
from “Simpson's Rule”
Why is Simpson’s rule more accurate than the trapezium rule?
a parabola bends with the curve where a chord only cuts across it
from “Simpson's Rule”
has solutions of the form
from “Separable Differential Equations”
, and y = 2 when x = 0. What is y?
from “Separable Differential Equations”
"Cools in proportion to how far it sits above the room" becomes
from “Forming Differential Equations”
"Leaks at a rate proportional to the volume left" becomes
kV
from “Forming Differential Equations”
If every segment in a column is identical, depends on
x only
from “Slope Fields”
In the slope field of , the segments on the y-axis are
horizontal
from “Slope Fields”
The Euler step rule is
from “Euler’s Method”
with y(0) = 1 and h = 0.5. After one step, y is
1.5
from “Euler’s Method”
For , what is the integrating factor?
from “The Integrating Factor”
For , what is the integrating factor?
from “The Integrating Factor”
The auxiliary equation has a repeated root m = 4. What is the solution?
from “The Auxiliary Equation”
What is the auxiliary equation of y″ − 5y' + 6y = 0?
from “The Auxiliary Equation”
For y″ − 3y' + 2y = 4x, what should the particular integral be tried as?
px + q
from “Complementary Function and Particular Integral”
What is the complementary function of y″ − 3y' + 2y = 4x?
Be
from “Complementary Function and Particular Integral”
The amplitude of a harmonic motion is doubled. What happens to the period?
nothing
from “Simple Harmonic Motion”
x = 5 cos 2t + 12 sin 2t. What is the amplitude?
13
from “Simple Harmonic Motion”
Under light damping, what happens to the amplitude?
it shrinks toward zero
from “Damped Oscillations”
Which case returns to rest fastest without passing through it?
critical
from “Damped Oscillations”