Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the rightmand' endpoints of the subintervals. x) = 7x x2 from x = 2 to x = 4; 2 subintervals Step 1 To approximate the area on the interval [a, b] using n subintervals, the width, along the x-axis, of each rectangle is given by (b a). The width of each rectangle will be LEE2 = I .I a: - 2 The height of each rectangle is given by the value of the function, F(x) = 7x x2, at the right-hand endpoint of each subinterval. The height of the rst rectangle, located on the subinterval [2, 3], is m = E - The height of the second rectangle, located on the subinterval [3, 4], is When the area under f(x) = x2+ x from x = 0 to x = 2 is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are as follows. 14 4 Left-hand endpoints: SL = 6 3 n 3n2 140-+ 18n + 4 Right-hand endpoints: Sp = 3n2 Use these formulas to find S, (14) and S(14). (Round your answers to two decimal places.) S (14) = 4.6068 X X Sp(14) = 4.7268Find the value of the sum. x , if x 1 = 9, X2 = -4, X3 = 3, X 4 = -2 Need Help? Read It [0/1.36 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 13.1.016.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the value of the sum. [ (12 + 5) Step 1 The summation means that we take the sum of /2 + 5 as / goes from 6 to 8. ( 12 + 5 ) = (62+ 5) + 1 1x 2+5+ (82 + 5) i =Use the sum formulas to express the following without the summation symbol. [ (1 -5 ) :) Step 1 First distribute the factor _. 4 n 3 Now we can use sum formula III. [ (x , + y p) = > The formula indicates that we can simplify each term in the summation separately. Apply the formula. -75 ) 4 1= 1 n Step 2 Next we use sum formula II. [cx, = [ x, (c = constant) Notice that in this situation n is treated as a constant because it does not depend on the index of summation, i. 412 4 4 n3 12 Step 3 The given sum has been rewritten as follows. Now, notice that (=) 1 is a constant multiple of the left side of Sum Formula I, which states that [1 = n. Apply the Sum Formula I. n(n + 1) (2n + 1) 6 Next, notice that (" ) is a constant multiple of the left side of Sum Formula V, which states that n(n + 1)(2n + 1) Apply the Sum Formula V. ER = (4)(2( +1)(20 + 1)) 6 4n(n + 1)(2n + 1) 6 2(n + 1)(2n + 1)