Evaluate the following indefinite integral. Use C for any constant of integration. da dæ x4/16x² – 25

Explain why you can omit the constant of integration when finding an integrating factor.

After an hour, the population of bacteria with a number of P0 found that their number became 3 / 2P0. If the growth rate is proportional to the number of bacteria (P (t) present at time t, find the time required for the number of bacteria to 3 times.

Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) xp

Solve for x x/12.4=4ft 6in/6ft 3 in

Complete the trig substitution to achieve an integral involving trig functions of 0. Stop here; do not integrate this function of 60: / Va? - 4 dr

Derek and Sandy leave an intersection at the same time. Derek travels north at 5 ft/s and Sandy travels west at 12 ft/s. Find a function that models the distance D between the pedestrians in terms of the time t (in seconds) elapsed since leaving the intersection.

Evaluate the indefinite integral using appropriate integration formula: Logarithm

An investment pays out 800,000 Mexican pesos per year, continuously for 5 years. Find the PV of the investment for r = 0.04 and r = 0.06.

A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 45 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.Suppose the object is displaced an additional 0.05 mm and released.Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2ms2 as the acceleration due to gravity.u(t) = 5·10−5(e−3t)sin(349.98t+π2​)mIncorrect  syntax error. Check your variables - you might be using an incorrect one. Submit QuestionQuestion 1