AP Calculus Exam Review

Integrals

100

∫(4x+4)dx

2x²+4x+C

200

∫(4x³-5x²+4)dx

x⁴-5x³/3+4x+C

300

∫4x⁶−2x³+7x−4 dx

4x⁷/7−x⁴/2+7x²/2−4x+C

400

∫(x²−1)(4+3x)dx

3x⁴/4+4x³/3−3x²/2−4x+C

500

∫500000 dx

500000x+C

Power/Quotient Rule

100

y=3x⁴-7x²+67

y^l=12x³-14x

200

y=67x²-10x+11x-6

y^l=134x+1

300

y=(3x+x⁴)/(2x²+1)

y^l=(4x⁵+4x³-6x²+3)/(2x²+1)²  

400

y=(x-x²)/(1+8x²)

y^l=(1-2x-8x²)/(1+8x²)²

500

Daily Double

y=(1+2x+3x²)(5x+8x²−x³)

y^l=(5+36x+90x²+88x³−15x⁴)

Differentiation of Trig

100

sin(x)

cos(x)

200

sec(x) 

sec(x)tan(x)

300

tan(x)

sec²(x)

400

Daily Double

tan(x)sec(x)

sec³(x)+sec(x)tan²(x)  

500

10tan(x)−2cot(x)

10sec²(x)+2csc²(x)

Limits

100

 limx->∞ (5x²+26-3x)/42+10x²

1/2

200

limx->∞ (10x²-10x+8)/100x+2x²

5

300

limx->0 ((6+x)²−36)/x

12

400

limx->2 (x³−7x²+10x)/(x²+x−6)

-6/5

500

limx->-1 (2x²-2)/(x+1)

-4

Random Equations

100

d/dx a^x

a^xlna

200

d/dx log_ax

1/xlna

300

d/dx a^u

a^uu^llna

400

d/dx arcsinx

1/sqrt(1-x²)

500

d/dx arctan(x)

1/1+x²