10 questions to be answered I need the answers separately and the work

Evaluate the integral Evaluate the indefinite integral. (2z + 8) (12 + 81 + 5)'da by making the substitutionju - x2 + 8x + 5. Consider the indefinite integral pezz +3 dx: a) This can be transformed into a basic integral by letting Integrate: 5x Vx - 4dx and du = b) Performing the substitution yields the integral c) Once we integrate and substitute, the final answer in terms of a is: A stone is thrown straight up from the edge of a roof, 650 feet above the ground, at a speed of 16 feet per second All answers are to the nearest tenth. A. Remembering that the acceleration due to gravity is -32 -, how high is the stone 6 seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground? ( Please note that the video below has units in *meters* rather Speedometer readings for a vehicle (in motion) at 5-second intervals are given in the table. t (sec) 0 5 10 15 20 25 30 v (ft/s) 0 5 18 33 41 40 29 Estimate the distance traveled by the vehicle during this 30-second period using Le, Re and My. Note that left and right approximations are using 6 intervals, while the midpoint approximation is using 3 intervals. a.)L6 = feet Approximate the area under the curve y = a from x = 2 to x = 5 using a Right Endpoint b.) R6 = feet approximation with 6 subdivisions and two decimal places. C.) M3 = feet Question Help vi Given the function graphed below, evaluate the definite integrals. The acceleration of an object (in m/s2) is given by the function a(t) = 7 sin(t). The initial velocity of the object is v(0) = - 12 m/s. a) Find an equation v(t) for the object's velocity. v(t ) = b) Find the object's displacement (in meters) from time t = 0 to time t = 3 rounded to 4 decimal places. JY meters c) Find the total distance traveled by the object from time 0 to time 3 rounded to 4 decimal places. [ f(z)da - meters