1. Sketch the region enclosed by the given curves and find its area. a) y = sin x; y = ex; x=0; X = b) y = Ixl; y = x - 2 c) x = 2y2; x = 4+y2d) 4x+ yz = 12; x =y 2 a) Show that F(x) = (x - 1)ex is an antiderivative of f (x) = xex. b) Sketch the region enclosed by the given curves and find its area. y = xex; y = ex (as x - -00)A B x+1 xl 1 _ x2 1 1. a) Find A and B so that 1 x21 b) Find the average value of the function for) 2 over the interval [0, i]. 1. The function graphed below has two zeroes at r and 3. Using Newton's Method with x1 = 9 as your initial approximation, illustrate the tangents used to find x2 and x3 and approximate x2 and x3. [3] 1. Find the general antiderivatives for the following: a) f (x) = sin(x) - 3x+ ex b) g (x) = - 6 x2 + 1 Vx 2. f' (x) = 3x2 + 4x - 1 and f(1) = 5. Find f (x).1. Use midpoints and n = 4 to approximate the integral: f15(x 1n x)dx Illustrate your approximation on the graph provided. l