These are the formulas needed so far for Mrs. Haubert's AP Calculus Memorization Quiz (Martin County High School).
Terms : Hide Images
| 146602789 | d sinu | cosu du | |
| 146602790 | d cosu | -sinu du | |
| 146602791 | d tanu | sec²u du | |
| 146602792 | d cotu | -csc²u du | |
| 146602793 | d secu | tanu*secu du | |
| 146602794 | d cscu | -cscu*cotu du | |
| 146602795 | ʃ sinu du | -cosu + C | |
| 146602796 | ʃ cosu du | sinu + C | |
| 146602797 | ʃ tanu du | -ln|cosu| + C | |
| 146602798 | ʃ cotu du | ln|sinu| + C | |
| 146602799 | ʃ secu du | ln|secu + tanu| + C | |
| 146602800 | ʃ cscu du | -ln|cscu + cotu| + C | |
| 146602801 | ʃ sec²u du | tanu + C | |
| 146602802 | ʃ csc²u du | -cotu + C | |
| 146602803 | ʃ secu*tanu du | secu + C | |
| 146602804 | ʃ cscu*cotu du | -cscu + C | |
| 146602805 | Pythagorean Identities (three of them) | sin²x+cos²x=1; 1+tan²x=sec²x; 1+cot²x=csc²x | |
| 146602806 | Ratio (two of them) | tanx=sinx/cosx; cotx=cosx/sinx | |
| 146602807 | sin2x | 2*sinx*cosx | |
| 146602808 | cos²x | (1+cos2x)/2 | |
| 146602809 | sin²x | (1-cos2x)/2 | |
| 146602810 | d arcsinu | du/√(1-u²) | |
| 146602811 | d arccosu | -du/√(1-u²) | |
| 146602812 | d arctanu | du/(1+u²) | |
| 146602813 | d arccotu | -du/(1+u²) | |
| 146602814 | d arcsecu | du/(|u|*√(u²-1)) | |
| 146602815 | d arccscu | -du/(|u|*√(u²-1)) | |
| 146602816 | ʃ du/√(a²-u²) | arcsin(u/a) + C | |
| 146602817 | ʃ du/(a²+u²) | 1/a*arctan(u/a) + C | |
| 146602818 | ʃ du/(u*√(u²-a²)) | 1/a*arcsec(|u|/a) + C | |
| 146602819 | (arc trig+value)=quad_____ | I | |
| 146602820 | ʃ du/u | ln|u| + C | |
| 146602821 | ʃ tan^(n)u du | tan^(n-1)/(n-1)u du - ʃ tan^(n-2)u du | |
| 146602822 | ʃ u dv | uv - ʃ v du | |
| 146602823 | arc trig - value=quad___if_____;quad__if____ | II, sec,cos,cot;IV, csc,sin,tan as negative | |
| 146602824 | variable to a variable power | ln both sides | |
| 146602825 | d(messwith */÷/power/root) | ln both sides | |
| 146602826 | Power of top>=power of bottom | divide | |
| 146602827 | Equation of line needs ___ & ___ | slope; point | |
| 146602828 | d(a^u) | a^u du*ln(a) | |
| 146602829 | ʃ a^u du | a^u/ln a + C | |
| 146602830 | Mean Value Theorem | Mc=Ml | |
| 146602831 | Definition of Derivative | lim Δx->0 (f(x+Δx)-f(x))/Δx | |
| 146602832 | Average Value Theorem | 1/(b-a)*ʃa,b f(x) dx | |
| 146602833 | Newton's | guess* f(guess)/f'(guess) | |
| 146602834 | Area of Trapezoid | 1/2*ln(b1+b2) | |
| 146602835 | Simpson's Rule | (b-a)/3n (1,4,2,4,1) | |
| 146602836 | d e^u | e^u du | |
| 146602837 | ʃ e^u du | e^u + C | |
| 146602838 | ʃ absolute value | use geometry | |
| 146602839 | Normal | perpendicular to tangent | |
| 146602840 | Length of Arc: Rectangular | ʃa,b √(1+[f'(x)]²) | |
| 146602841 | Length of Arc: Polar | ʃa,b √([f(Θ)]²+[f'(Θ)]²) | |
| 146602842 | Length of Arc: Parametric | ʃa,b √([dy/dt]²+[dx/dt]²) | |
| 146602843 | Surface Area | 2π*ʃa,b r"*L | |
| 146602844 | Polar x=______ | rcosΘ | |
| 146602845 | Polar y=______ | rsinΘ | |
| 146602846 | Area in Polar | 1/2*ʃa,b r² dΘ | |
| 146602847 | F=___when Work=_____ | k*d; ʃ k*x dx | |
| 146602848 | Differentials | get x's with dx's and y's with dy's | |
| 146602849 | Absolute Maximum/Minimum | highest/lowest y values | |
| 146602850 | d/dx ʃa,x² f(t) dt | f(x²)*2x | |
| 146602851 | slope | derivative |
