Integration by Parts
Trig Substitution
Arc Length of a Curve
Differential Equations
100
Integrate the following:
intxe^xdx
xe^x-e^x+C
100
Lobotomy Zone Question: 500 Points Each
As of right now, who are my two favorite Umas in Umamusume: Pretty Derby
Oguri Cap & Vodka
100
Compute the arc length [1,4]:
2/3(x^2+1)^(3/2)
45
100
Find the general solution to the following:
dy/(dx)=x^3/y^2
y^3/3=x^4/4+C
y=root(3)((3x^4)/4+C
200
Integrate the following:
intx^5lnxdx
1/6x^6lnx-1/36x^6+C
200
Integrate the following:
int1/sqrt(1-x^2)dx
arcsinx+C
200
Compute the arc length [1,3]:
x^3/6+1/(2x)
14/3
200
Find the general solution to the following:
dy/dx=3e^(x-y)
e^y=3e^x+C
y=ln(3e^x+C)
300
Integrate the following:
intsinxcosdx
sin^2x/2+C
300
Integrate the following:
int1/(x^2sqrt(x^2+4))dx
-sqrt(x^2+4)/(4x)+C
300
Compute the arc length [-2,2]:
sqrt(4-x^2)
2pi
300
Find the particular solution of the DE:
dy/dx=(2x)/y^2,y(2)=root(3)(13)
y^3/3=x^2+1/3
y=root(3)(3x^2+1
400
Integrate the following:
int_1^9lnx/sqrtxdx
6ln9-8
400
Integrate the following:
intsqrt(1+x^2)/x
ln|sqrt(x^2+1)/x-1/x|+sqrt(x^2+1)
400
Compute the arc length [1,2]:
x^2-1/8lnx
3+1/8ln2
400
Find the particular solution of the DE:
dy/dx=1/(sec^2y),y(3)=0
tany=x-3
y=arctan(x-3)
500
Integrate the following:
int_0^(pi/4)xsin2xdx
1/4
500
Integrate the following:
int_0^ax^2sqrt(a^2-x^2)dx
(a^4pi)/16
500
Compute the arc length [0,1]:
x^(3/2)
(13sqrt13-8)/27
500
Find the particular solution of the DE:
dy/dx=-1/siny,y(3)=pi/2
cosy=x-3
y=arccos(x-3)