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Consider the integral 3 +1) dx (a) Find the Riemann sum for this integral using right endpoints and n = 4. %3D (b) Find the Riemann sum for this same integral, using left endpoints and n = 4

Consider the integral 3 +1) dx (a) Find the Riemann sum for this integral using right endpoints and n = 4. %3D (b) Find the Riemann sum for this same integral, using left endpoints and n = 4

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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Consider the integral 3 +1) dx 5. (a) Find the Riemann sum for this integral using right endpoints and n = 4. (b) Find the Riemann sum for this same integral, using left endpoints and n = 4
Transcribed Image Text:Consider the integral 3 +1) dx 5. (a) Find the Riemann sum for this integral using right endpoints and n = 4. (b) Find the Riemann sum for this same integral, using left endpoints and n = 4
Expert Solution
Step 1

Given : Integral

          ∫593x+1dx

We have to find Riemann sum using the right endpoints and left endpoints with n=4

Pre-requisite : 

P1. The right Reimann sum is given by

      ∫abfxdx≈∆xfx1+fx2+.......+fxn-2+fxn-1+fxn

where ∆x=b-an.

P2. The left Reimann sum is given by

     ∫abfxdx≈∆xfx0+fx1+fx2+.......+fxn-2+fxn-1

where ∆x=b-an.

Here, we have

a=5, b=9, fx=3x+1, n=4

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