Calc BC

Integration

100

int1/(9+x^2)dx

1/3arctan(x/3)+c

200

intx^3cos(x)dx

x^3sin(x)+3x^2cos(x)-6xsin(x)-6cos(x)+c

300

inte^(2x)cos(x) dx

1/5e^(2x)sin(x)+2/5e^(2x)cos(x)+c

Diff Eq

100

x^2 + 4y^2 = 7 + 3xy

Find 

dy/dx

(3y-2x)/(8y-3x)

200

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

300

Find the general solution of the differentable equation

tdy/dx=cos(t)-2y

for

t>0

y=(tsin(t)+cos(t)+c)/t^2

Parametric

100

find the slope of the tangent line at t=3

dx/dt=2t^2+t

dy/dt=sin(t^2)

≈ 0.032

200

Find the speed at t=4

dx/dt=(sqrt(t+2))/e^t

dy/dt=sin^2(t)

 0.575

300

find the arclength from

0<=t<=pi/2

x=e^-tcos(t)

y=e^-tsin(t)

1.12

polar

100

Find the slope of the curve at 

theta=pi/2

r=4-2sin(2theta)

m=-1

200

Find the surface area created by revolving

r=5-4sin(theta)

about the polar axis from 

0<=theta<=pi

79.846

300

find the area inside

r=2cos(theta)

and outside 

r=1

sqrt3/2+pi/3 or ≈1.9132