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n(n+1) and T(n+ 1)(2n + 1) 6. -1 Student solution. We begin by constructing a partition for the intervali into n equal segments. The width of each segment is Az = The partition points are as follows: Io = , In with the general term z given by Ik = From each segment [-1, I] with k = 1,2,...n in this partition, we choose r as the right-end point, namely Then we have that %3D We form the Riemann sum R, which is given by, Using the sum formulas according to the hint above, we simplify the Riemann sum to R, Next we have that lim R, This we obtain the integral equals (3z + 12r) dr

n(n+1) and T(n+ 1)(2n + 1) 6. -1 Student solution. We begin by constructing a partition for the intervali into n equal segments. The width of each segment is Az = The partition points are as follows: Io = , In with the general term z given by Ik = From each segment [-1, I] with k = 1,2,...n in this partition, we choose r as the right-end point, namely Then we have that %3D We form the Riemann sum R, which is given by, Using the sum formulas according to the hint above, we simplify the Riemann sum to R, Next we have that lim R, This we obtain the integral equals (3z + 12r) dr

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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n(n+1) and n(n+1)(2n+1) 6 k%3D1 Student solution. We begin by constructing a partition for the interval into n equal segments. The width of each segment is The partition points are as follows: with the general term given by Ik From each segment [-1, T] with k = 1,2,...n in this partition, we choose r as the right-end point, namely Then we have that f(r) =| We form the Riemann sum R, which is given by, R, = k1 Using the sum formulas according to the hint above, we simplify the Riemann sum to R, Next we have that lim R, This we obtain the integral equals (3x2 + 12r) da
Transcribed Image Text:n(n+1) and n(n+1)(2n+1) 6 k%3D1 Student solution. We begin by constructing a partition for the interval into n equal segments. The width of each segment is The partition points are as follows: with the general term given by Ik From each segment [-1, T] with k = 1,2,...n in this partition, we choose r as the right-end point, namely Then we have that f(r) =| We form the Riemann sum R, which is given by, R, = k1 Using the sum formulas according to the hint above, we simplify the Riemann sum to R, Next we have that lim R, This we obtain the integral equals (3x2 + 12r) da
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