Mr. Orchard’s Math 142 WIR 6.1-6.3 1. Find the most general antiderivatives for the following functions: (a) f 0 (x) = 8x9 (b) g 0 (x) = 6x + 9x7 + 2 (c) k 0 (x) = 6 u2 (d) h0 (x) = 8+u2 u + 3 u Week 10 Mr. Orchard’s Math 142 WIR 6.1-6.3 2. Evaluate the following indefinite integrals. R 2 (a) + 4x34 − x17 dx x (b) R (c) R 6e−x +14 (d) R (t5 − 4et ) dt e−x dx (6x − 10)12 dx Week 10 Mr. Orchard’s Math 142 WIR 6.1-6.3 3. Use u-substitution to evaluate the following indefinite integrals: R (a) e−9x dx (b) R 3x7 (x8 + 3)9 dx (c) R x5 dx x6 +4 (d) R (6x2 − 9)e6x 3 −27x dx Week 10 Mr. Orchard’s Math 142 WIR 6.1-6.3 4. Find f (x) given the following information: (a) f 0 (x) = 12x2 + 8x + 4, f (2) = 58 (b) f 0 (x) = (ln(x))48 , x (c) f 0 (x) = x , x2 +3 (d) f 0 (x) = 10e x x2 f (1) = 10 f (2) = 0 −2 , f (−2) = 10 − 5e Week 10 Mr. Orchard’s Math 142 WIR 6.1-6.3 Week 10 5. An object travles with velocity v(t) = (t − 1)2 + 1. Using n = 3 and equal subintervals, estimate the distance traveled by the object on the interval [0, 3] with a right-hand sum. 6. An object travels at a velocity given by v(t) = t2 − 2t + 2 feet per second. Using n = 5 and equal subintervals, find the following estimations for the distance the object traveled on the interval [0, 1]. (a) Upper bound approximation (b) Lower bound approximation Mr. Orchard’s Math 142 WIR 6.1-6.3 Week 10 7. During regular intervals the Millenium Falcon’s speed was calculated during the Kessel Run. Han Solo (the pilot) steadily increased his speed throughout the flight. The information is summarized in the chart below. Use this chart to estimate the distance Han Solo flew during this instance of the Kessel Run, with n = 8 equal subintervals and a right hand sum. t (in seconds) v(t) (in parsecs per second) 0 0 2 0.45 4 0.53 6 0.66 8 0.78 10 0.80 12 0.82 14 0.83 16 0.88 Mr. Orchard’s Math 142 WIR 6.1-6.3 Week 10 8. An object has a velocity v(t) = 2t + 50 feet per second. Use n = 6 and equal subintervals to compute the following approximations of the distance the object traveled starting one second after it starts and ending 12 seconds later. (a) Left-hand sum approximation (b) Right-hand sum approximation (c) Average of the two sums Mr. Orchard’s Math 142 WIR 6.1-6.3 Week 10 9. Speedometer readings (in feet per second) for a motorcylce at 12-second intervals are given in the table below: t v(t) 0 32 12 28 24 25 36 22 48 24 60 28 (a) Estimate the distance traveled by the motorcycle during this time using a left hand sum with n = 5. (b) Estimate the distance traveled by the motorcycle during this time using a right hand sum with n = 5.