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Estimate the minimum number of subintervals to approximate the value of (31 + 5t) dt with an error of magnitude less than 10 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is O. (Round up to the nearest whole number.)

Estimate the minimum number of subintervals to approximate the value of (31 + 5t) dt with an error of magnitude less than 10 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is O. (Round up to the nearest whole number.)

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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2 Estimate the minimum number of subintervals to approximate the value of (3t° + 5t) dt with an error of magnitude less than 10 - 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is (Round up to the nearest whole number.)
Transcribed Image Text:2 Estimate the minimum number of subintervals to approximate the value of (3t° + 5t) dt with an error of magnitude less than 10 - 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is (Round up to the nearest whole number.)
Expert Solution
Step 1

The give integral is:

∫023t3+5tdt

Let f(t) be the integrand and a and b be the left and right limits of the integral:

f(t)=3t3+5t, a=0,  b=2

Let n be the desired subinterval.

The error magnitude E is given as,

E=10-4

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