Problem 8. Evaluate the integral: J (5-x2 -4Vx)dx =? (Show work!) Problem 9. The graph of the function f(t) is given on the left and the graph of the function g(t) is given on the right. Using the graphs and the information about the area between the graph and the x-axis calculate: y = S(1 ) 10 y = g(1) Area = 3 16 10 11 + Area = 35 Area = 27 a) J f (n) dt + ( 8 (1 )dt = b ) ( 2 f ( 1 ) - 3 8 (1 ) dt = d) S 2 8 ( 1 ) dt = 666/ Problem 10. Find - da-999 if y = cosx (Show work!)Problem 13. Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. [Show work and all steps of the second derivative test] Ax) = -e (x+ 7 ) Problem 14. Use the First Derivative Test to determine the local maxima, local minima of the given function and the intervals on which it is increasing/decreasing. [Show work and all steps of the first derivative test] A(x ) = -ex (x + 7 ) Problem 15. The graph of the function f(x) is given on the picture on right. a) Calculate using geometry b) Confirm the answer from a) by solving the integral below using the Fundamental Theorem of Calculus (3x - 1) dx =Problem 11. For the functions f(x) -x - 3x and g(x) = e let h(x) - Ag(x)). a) Calculate h(x) - ? (Show work! Simplify!) b) h' (x) =? (Show work!) c ) [hex)dx = ? (Show work!) Problem 12. Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. [Show work and all steps of the concavity test] (x) = 3x5 - 25x4+ 40x3+ 110