Since the integral y(x) = Sof(t) dt with variable upper limit satisfies (for continuous f) the initial value problem y' = f(x), y(0) = 0, %3D any numerical scheme that is used to approximate the solution at x = 1 will give an approximation to the definite integral %3D 1 f(t) dt . 0. Derive a formula for this approximation of the integral using Euler's method.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Since the integral y(x) = Jf(t) dt with variable
upper limit satisfies (for continuous f) the initial value
problem
y' = f(x).
y(0) = 0,
any numerical scheme that is used to approximate the
solution at x = 1 will give an approximation to the
definite integral
f(t) dt .
Derive a formula for this approximation of the integral using
Euler's method.
Transcribed Image Text:Since the integral y(x) = Jf(t) dt with variable upper limit satisfies (for continuous f) the initial value problem y' = f(x). y(0) = 0, any numerical scheme that is used to approximate the solution at x = 1 will give an approximation to the definite integral f(t) dt . Derive a formula for this approximation of the integral using Euler's method.
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