Partial Fraction Integration
Integration by Parts 1
Integration by Parts 2
Rapid Repeated Integration by Parts
Volume by Cylindrical Shells
100
If the numerator is larger than the denominator what must the first step be?
Polynomial Long Division
100
When is integration by parts used?
When an integral involves the product of two functions and can’t be solved by u-sub.
100
How many times will you integrate by parts in this equation?
intx³sin(x)dx
3 times
100
When writing the chart, do you start with a positive sign or negative sign?
Positive sign
100
Volume by Cylindrical Shells differs from the disc and washer because we integrate _____ to the axis of rotation
Parallel
200
What would the ‘[A]’ matrix in your calculator look like in order to solve this system of equations assuming the columns are alphabetical?
A+3B=9
C+2A = 13
B+C=-3
200
What is the formula for Integration by Parts?
intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx
or
intudv=uv-intvdu
200
What is the next step in this equation?
inte^xsin(x)dx=-e^xcos(x)+e^xsin(x)-inte^xsin(x)dx
Add the
inte^xsin(x)dx
to both sides
200
In this integral, which should you assign as the dv and which as the u? int(e^x)x^200dx
u=x^200
dv=e^x
200
When a function is being revolved around the y axis and it is touching the y axis, what is the equation of the r(x) function? V=int_a^b2pir(x)f(x)dx
r(x)=x
300
What would the setup for partial fraction decomposition look like for this equation
(10x+2025)/[(x^2+3)^2(x+5)
in terms of letters?
(Ax+B)/(x^2+3)+(Cx+D)/(x^2+3)^2+E/(x+5)
300
In this integral, which should you assign to be f(x) and which to g’(x)? intxcos(x)dx
f(x)=x and g'(x)=cos(x)
300
What identity do you use to solve this integration by parts intcot²(x)dx ?
cot²(x)=csc²(x)-1
300
What is the coefficient of the last term (other than C) in this integral? intx^4sin(4x)dx
-3/128
-24/1024
300
When finding the volume of a solid generated by revolving the region bounded by y=x^(1/3) ; x=0 ; and x=8 around the x-axis, what are the bounds of the integral?
0 to 2
400
(5 min Calculator) Perform Partial Fraction Decomposition on this equation
(x^2-2x-35)/[(x+3)(x-4)(x+9)]
10/[21(x + 3)] - 27/[91(x - 4)] + 32/[39(x + 9)]
400
3min Solve this integral intln(x)+xcos(x)dx
x*ln(x) - x + x*sin(x) + cos(x) + C
400
4 min (No calculator) Solve the following int_0^pix²sin(x)dx ?
pi^2-4
400
Solve the following equation(Calculator): inte^(x/2)x^2dx
2x^2e^(x/2)-8xe^(x/2)+16e^(x/2)+C
400
(Calculator) Find the volume of a solid generated by revolving the region bounded by y = 5x, x = 0, and x = 3, when rotated around the x-axis.
225pi
or
1413.717
500
(3min) Solve this integral ∫(x + 4)/(x^2 + x - 30) dx
(2/11) * ln|x + 6| + (9/11) * ln|x - 5| + C
500
(2min No Calc) Solve this integral int_0^ex^2ln(x)dx
2/9e^3
500
4 min Solve the following intx^2sin^2(x)dx
x^3/6-(x^2sin(2x))/4-(xcos(2x))/4+sin(2x)/8+C
500
Solve the following equation(Calculator): intx^5cos(3x)dx
1/3x^5sin(3x)+5/9x^4cos(3x)-20/27x^3sin(3x)-20/27x^2cos(3x)+40/81xsin(3x)+40/243cos(3x)+C
500
(Calculator) Find the volume of a solid generated by revolving the region bounded by x = 2y^(1/2) and y = 6 , when rotated around the y-axis.
72pi
or
226.195