n d = n+1 + c logee2 = 2logee = 2 logek = logek + loge loge = loge ½ = ½ loge Area between curve and axis loge/k = loge - logek A = ba f() d Volume of revolution V = ba [ f() ]2 d Trigonometric Functions Arc length Area between two curves l = rΘ A = top curve - bottom curve area of sector A = ½ r2Θ Volume between two curves y = sin A = (top curve)2 (bottom curve)2 – Period = 2 Approximating integrals Amplitude = 1 y = cos Simpson’s Rule A = h [ f(a) + 4 x f((a+b)/2) + f(b) ] 3 Trapezoidal Rule A = ½ h [ f(a) + f(b) ] Logarithmic and Exponential Period = 2 Functions Amplitude = 1 Exponential functions y = tan e = e ec = cec ef() = f’() ef(x) e d = e + k Period = ec d = ec + k = 1 Derivatives Logarithmic Functions sin = cos loge = cos = -sin logef() = tan = sec2 Integrals d = loge = c sina d = -1/a cos + c cosa d = 1/a sin + c d = logef() + c sec2a d = 1/a tan + c Log laws Rates of Change
n d = n+1 + c Area between curve and axis A = ba f() d Volume of revolution V = ba [ f() ]2 d Area between two curves A = top curve - bottom curve Volume between two curves A = (top curve)2 – (bottom curve)2 Approximating integrals Simpson’s Rule A = h [ f(a) + 4 x f((a+b)/2) + f(b) ] 3 Trapezoidal Rule A = ½ h [ f(a) + f(b) ] Logarithmic and Exponential Functions Exponential functions e = e ec = cec ef() = f’() ef(x) e d = e + k ec d = ec + k Logarithmic Functions loge = logef() = d = loge = c d = logef() + c Log laws logee2 = 2logee = 2 logek = logek + loge loge = loge ½ = ½ loge loge/k = loge - logek Trigonometric Functions Arc length l = rΘ area of sector A = ½ r2Θ y = sin Period = 2 Amplitude = 1 y = cos Period = 2 Amplitude = 1 y = tan Period = = 1 Derivatives sin = cos cos = -sin tan = sec2 Integrals sina d = -1/a cos + c cosa d = 1/a sin + c sec2a d = 1/a tan + c Rates of Change