Integration
int1/(9+x^2)dx
1/3arctan(x/3)+c
x^2 + 4y^2 = 7 + 3xy
Find
dy/dx
(3y-2x)/(8y-3x)
find the slope of the tangent line at t=3
dx/dt=2t^2+t
dy/dt=sin(t^2)
≈ 0.032
Find the slope of the curve at
theta=pi/2
r=4-2sin(2theta)
m=-1
intx^3cos(x)dx
x^3sin(x)+3x^2cos(x)-6xsin(x)-6cos(x)+c
use Euler's Method with a step size of 0.25 to approximate y(1) if y(0)=2 and
dy/dx=1/2x-y
y(1)≈0.791015625
Find the speed at t=4
dx/dt=(sqrt(t+2))/e^t
dy/dt=sin^2(t)
0.575
Find the surface area created by revolving
r=5-4sin(theta)
about the polar axis from
0<=theta<=pi
79.846
inte^(2x)cos(x) dx
1/5e^(2x)sin(x)+2/5e^(2x)cos(x)+c
Find the general solution of the differentable equation
tdy/dx=cos(t)-2y
for
t>0
y=(tsin(t)+cos(t)+c)/t^2
find the arclength from
0<=t<=pi/2
x=e^-tcos(t)
y=e^-tsin(t)
1.12
find the area inside
r=2cos(theta)
and outside
r=1
sqrt3/2+pi/3 or ≈1.9132