Please provide answers and explanations for the attached 8 questions.

\fQuestion 2 (Essay Worth 10 points) (05.03) Find tan x2 )dx . dx 2Question 3 (Essay Worth 10 points) (06.01) Find the area bounded by the curves x = y2 - 4y and x = 2y - y2. Your work must include an integral in one variable.Question 4 (Essay Worth 10 points) (06.02) Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x2 and y = x about the line x = 5.Question 5 (Essay Worth 10 points) (06.03) A ball is thrown upward with a speed of 40 feet per second from the edge of a cliff 500 feet above the ground. What is the speed of the ball when it hits the ground? Use acceleration due to gravity as 32 feet per second squared and approximate your answer to 3 decimal places. [E21 Question 6 (Essay Worth 10 points) (07.03) Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = -x. Question 7 (Essay Worth 10 points) (08.02) Electricity is consumed between the hours of midnight (t = 0) and 6 am. (t = 6). Selected values of the rate of consumption are shown in the table below, with t measured in hours past midnight, and R(t) measured in KW per hour. Use 4 trapezoids to estimate the total amount of electricity to the nearest KW consumed between midnight and 6 am. t (hours) 0 1 2 5 6 R(t)KW/hr 400 200 350 200 150 Question 8 (Essay Worth 10 points) (08.03) 5x Show that the function F(x)=J1dt is constant on the interval (0, +00). t X Sorry, question 8 was overlooked. I am giving the solution: show that the function F(x) = - It is constant 20c dt = In (t ) SX - ( - = On (sx) - In(220) Using logarithm property [ en(m) - Incn) = In () Then en (sx) - In (2x) = lan ( 5x) [) = On (5) Po ( S ) = In ( 2.5) is a constant in the inared (0,+0)