Use the following theorem to evaluate the given integrals. Theorem: If f is integrable on a...

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Use the following theorem to evaluate the given integrals. Theorem: If f is integrable on a closed interval containing the three points a, b, and, c then cb C [ f(x) dx = [ f(x) dx + [ f(x a a no matter how the points are ordered. NOTE: Enter the exact answers. 3 (a) [6 + |x|dx = (b) 631/1/2 0 cos x dx = [ f(x) dx Let F(x) = S + 144dt. Find the following. Enter the exact answers. (a) F(5) = i (b) F' (5) = (c) F" (5): = i Let F(x) = x = 0 Find the value of x where F attains its minimum value. i x t - 4 -dt for0 < x < 0. t + 8 A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she estimates that between 4:30 P.M. and 5:30 P.M. the rate R(t) at which cars enter the highway is given by the formula 130(1 0.0001t) cars per minute, where t is the time (in minutes) since 4:30 P.M. R (t) = (a) When does the peak traffic flow into the highway occur? t = i (b) Determine the number of cars that enter the highway during the rush hour. i cars will enter the highway during the rush hour. Use the following theorem to evaluate the given integrals. Theorem: If f is integrable on a closed interval containing the three points a, b, and, c then cb C [ f(x) dx = [ f(x) dx + [ f(x a a no matter how the points are ordered. NOTE: Enter the exact answers. 3 (a) [6 + |x|dx = (b) 631/1/2 0 cos x dx = [ f(x) dx Let F(x) = S + 144dt. Find the following. Enter the exact answers. (a) F(5) = i (b) F' (5) = (c) F" (5): = i Let F(x) = x = 0 Find the value of x where F attains its minimum value. i x t - 4 -dt for0 < x < 0. t + 8 A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she estimates that between 4:30 P.M. and 5:30 P.M. the rate R(t) at which cars enter the highway is given by the formula 130(1 0.0001t) cars per minute, where t is the time (in minutes) since 4:30 P.M. R (t) = (a) When does the peak traffic flow into the highway occur? t = i (b) Determine the number of cars that enter the highway during the rush hour. i cars will enter the highway during the rush hour.