1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.
1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.
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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Transcribed Image Text:1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.
2. Write the given (total) area as an integral.
a. The area above the x-axis and below y = 4 - x²
b. The area above the x - axis and below y = 4x - x²
c. The area between y = sin x and the x
axis for 0 ≤ x ≤ T
3. Compute
f(x) dx
f(x) = {
2x if x < 1
4 if x ≥ 1
4. Find the integral of your answer in problems 2a and 2b.
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