Homework for applied calc 2. This homework was assigned on web assign and you have to evaluate the integral.

Evaluate the integral. [14m Wax Evaluate the integral, using Integration by Part5. lnx fx3dx E +6 Need Help? i i Evaluate the indenite integral. [Fe9'0? E \"3 Need Help? ii Compute the denite integral. 5 / xezx dx 0 Need Help? ii Use a calculator (or computer software) to estimate the value of the denite integral. Round to three decimal places. 4 fOVr3+rdr Need Help? ii A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation mrt m v(t) = gt ve |n where g is the acceleration due to gravity and t is not too large. Ifg = 9.8 m/sz, m = 30,000 kg, r = 130 kg/s, and ve = 3,200 m/s, nd the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.) I'T'I Need Help? - First make a substitution and then use integration by parts to evaluate the integral. f tsc'a't E + C Need Help? i i i 4 Suppose that ((1) = 3, f(4) = 9, f '(1) = 5, f '(4) = 3, and f " is continuous. Find the value of f xf "()0 dx- 1 Need Help