MAT-1120 Midterm: MATH 1120 App State Spring2014 Test2 answer key
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Be sure to show your work! (a) consider i =z 6. [don"t worry about simplifying. ] sin(ln(x2 + 1)) dx. Write down the midpoint approximation for i if n = 3 (i. e. m3). We need to break the interval [ 3, 6] into n = 3 pieces. Notice that x = are: x0 = 3 < x1 = 0 < x2 = 3 < x3 = 6. To get midpoints we need to move x/2 = 3/2 from the end of each subinterval. This gives us the following midpoints: x 1 = 3 + 3/2 = 3/2, x 2 = 0 + 3/2 = 3/2, and x 3 = 3 + 3/2 = 9/2. 3 sin(ln(x2 + 1)) dx m3 = x(cid:0)sin(ln((x 1)2 + 1)) + sin(ln((x 2)2 + 1)) + sin(ln((x 3)2 + 1))(cid:1) = 0 e x2/4 dx. (the graph of y = e x2/4 is decreasing and concave down on [0, 2]. )
