Integrals
Derivatives
Limits
Area
Misc.
100

∫cotxcscxdx=

What is -cscx+c

100

The derivative of x2+9x-4=

What is 2x+9

100

lim x+3 as x->1

What is 4

100

The formula for area between 2 curves

 What is ∫[f(x)−g(x)]dx

100

The average rate of change of the function f(x)=x4-5 on the closed interval [0, 3]

What is 27

200

∫(3/x)dx=

What is 3lnlxl+c

200

The derivative of sinxcosx=

cos2(x)-sin2(x)

200

lim (x-3)/(x2-9) as x->3

What is 1/6

200

The area of the region bounded by f(x)=x2+2x+1 and g(x)=2x+5

What is 10.667

200

The first three non-zero terms of the maclaurin series of sinx

What is x-x3/3!+x5/5!

300

∫1/(x2+4x+3)dx=

What is (1/2)(lnl(x+1)/(x+3)l)+c

300

The derivative of e(-4x+2)

What is -4e(-4x+2)

300

lim (4x+3x2)/(2x-6x2) as x->∞

What is -1/2

300

The area of the region bounded by f(x)=x2 and g(x)=6-x

What is 20.833

300

Given 3x2+2xy+y2=1, dy/dx=

What is -(3x+y)/(x+y)

400

∫arctanxdx=

What is xarctanx-(1/2)(lnl1+x2l)+c

400

The derivative of arctanx=

1/(1+x2)

400

lim (x3+x2-4x)/(x9+3x12-3x) as x->0

What is 4/3

400

The area of the region enclosed by r=3(1+cos(θ))

What is 27pi/2

400

The first three non-zero terms of the maclaurin series of ln(1-x)

What is -x-x2/2-x3/3

500

∫xexdx=

What is xex-ex+c

500

The derivative of sin(x2-4x)=

What is (2x-4)cos(x2-4x)

500

lim (x2+2x-4)/(9x-2) as x->∞

What is ∞

500

The area of the region bounded by f(x)=(cos(πx/10))1/2, x=-7, x=7, y=2, and the x-axis

What is 20.372

500

The volume of the solid generated by revolving the region bounded by y=x, y=3, and x=0 about the line y=4.

What is 18π

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