11 questions to be answered I want the answers separately and the work

Express the limit lim (3 sin (2Tz; ) + 8) Ax; over [1, 6) as an integral. Provide a, b and f(x) in the expression / f(x)dr. a = b =f(z) = Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. Enter an exact value. Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area, to the nearest tenth, using geometry. 18x - 3/dx 3 Evaluate the integral below by interpreting 2- y=f(x) it in terms of areas in the figure. A1 A3 The areas of the labeled regions are 2 0 3 15 A2 7 A4 10 A1 - 8, A2 - 4, A3 - 2 and A4 - 2 To find the blue shaded area above, we would calculate: (figure is NOT to scale) v = [ f(= ) dz [ f(z)de = area Where: V = a=. b = [10 Given the function graphed below, evaluate the definite integrals. f( x ) = Area = 2 Given that f(x)dx - 18. what is f f(u)dur Enter a reduced fraction. f(x) de = answer = cos(x)In (1 + x2) + 236 Evaluate 1 + el.72x -78 da. Enter an exact answer. answer = Given p(s) ds - 19 and p(s)ds = 5.8, evaluate the following integral. P(s) ds - Find the average value fave of f(x) = x between -1 and 1, then find a number c in [-1,1] where f(c) = fave. fave = C = Find the exact average value fave of f(x) = V4 - x2 between 0 and 2, then find an exact number cin [0,2] where f(c) = fave. fave =