Unit 6
Solve the following integral:
int[3, x] (2t/t2)dt
What is 2ln(x/3)?
This is the area of the region bounded by y=x2 and y=x3.
What is 1/12?
Find the general solution to this differential equation: dy/dx = (x2+2)/3y2
What is y=cbrt[(1/3)x3+2x+C]?
These two numbers are used most often to describe time and/or question numbers in reference to this popular 2025 meme.
What are 6 and 7?
DAILY DOUBLE!!
This variable substitute for “X” is found commonly in nature and is a staple of spring.
What is a flower?
Find the general solution:
int (9x2+8r7)dr
What is 9x2r+r8+C?
Find the volume of the solid formed by rotating around the y-axis, y=1+sqrt(x), x=0, y=3.
(calculator allowed)
What is 32pi/5 or 20.106?
Find the solution to dy/dx = (3-x)/y, with an initial condition y(6)=-4.
What is y=-sqrt(6x-x2+16)?
This material was used to form models of what?
What are playdough models of the washer method?
A group of adolescents, colloquially.
What are children?
The table below shows the number of male birds per day that arrive at a certain nesting area, where M(t) is measured in number of birds per day. Select values of M(t) are shown in the table below:
t (days) M(t) (birds per day)
0 2
5 7
10 16
15 6
20 5
25 2
30 0
Using a midpoint Riemann sum with intervals [0, 10], [10, 20], and [20, 30], estimate int[0, 30] M(t)dt.
What is 150?
The base is the region enclosed by y=x2 and y=3. Find the volume of the solid when the cross section perpendicular to the y-axis are semicircles. (calculator allowed (ฅ^>⩊<^ ฅ) )
What is
Draw the slope field of dy/dx = -x/y.
What is a slope field in the shape of a circle?
This cartoon character is Ms. Won’s favorite, and the subject for many Desmos Graph projects.
Who is Snoopy?
This variable substitute for “X” is commonly featured in the night sky, also found in one of Van Gogh’s most famous paintings.
What is a star?
Solve the following integral using U-substitution:
int((1+e3x)/(e3x+3x))dx
What is (1/3)ln(abs(e3x+3x))+C?
The base of a solid is bounded by y=x3, y = 0, and x = 1. Find the volume of the solid for an equilateral triangle cross section taken perpendicular to the y-axis.
What is sqrt(3)/40?
P'=r(P-N/r), P(t)=balance in the annuity, r=interest rate, N=withdrawal rate
A continuous annuity with withdrawal rate N = $5,000/year and interest rate r = 5% is funded by an initial deposit of P0=$50,000.
This is the balance in the annuity after 10 years.
What is $17,563.94?
This movie-turned-Broadway show has this iconic line about calculus.
What is “The limit does not exist!” from Mean Girls?
This question poses an integer answer through a homophone of this teacher’s last name.
What are “What’s my last name?” and Ms. Won
A toy car moves along the y-axis with velocity given by the equation, v(t) = tsin(t2) for t >= 0. This is the car’s acceleration, in unit/sec at t = 1.5.
What is -2.050 units/sec?
DAILY DOUBLE!!
Find the volume of the region enclosed by y = x − 1, y = 0, x = 3 if it’s rotated about the line x = 5.
(no calculator allowed ദ്ദി(˵ •̀ ᴗ - ˵ ) ✧)
What is 32pi/3?
Find the solution of the differential equation that satisfies the given condition.
dy/dx= (x-1)/x2y, y(1)=-4
What is y=-sqrt(2ln|x|+2/x+14)?
This misspelling of these two words turned many to brief panic during Spork Royale.
What is Safe Zine?
This variable substitute for “X” is a substitute in its most unoriginal, unchanged form. Also used to refer to items and happenstances of situations.
What is "something"?