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form" of the Fundamental Theorem of Calculus: Let f : [xo, x1] → R be a continuous function. Then if F : [x0,x1] → R is the function defined by the integral F(æ) = | s(t)dt, it follows that d F'(x) = dx f(t)dt = f(x).

form" of the Fundamental Theorem of Calculus: Let f : [xo, x1] → R be a continuous function. Then if F : [x0,x1] → R is the function defined by the integral F(æ) = | s(t)dt, it follows that d F'(x) = dx f(t)dt = f(x).

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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form" of the Fundamental Theorem of Calculus: Let f : [xo,x1] → R be a continuous function. Then if F : [x0,x1] → R is the function defined by the integral F(x) = it follows that d F'(x) = : f(t)dt = f(x). dx
Transcribed Image Text:form" of the Fundamental Theorem of Calculus: Let f : [xo,x1] → R be a continuous function. Then if F : [x0,x1] → R is the function defined by the integral F(x) = it follows that d F'(x) = : f(t)dt = f(x). dx
3. Show that 1 =dt t3 +1 y = is an implicit solution of the IVP 2y" – 32 (y')² = 0, y(0) = 0, y'(0) = 1. Assume x > 0. Hint: Recall what is most commonly referred to as the "first 1
Transcribed Image Text:3. Show that 1 =dt t3 +1 y = is an implicit solution of the IVP 2y" – 32 (y')² = 0, y(0) = 0, y'(0) = 1. Assume x > 0. Hint: Recall what is most commonly referred to as the "first 1
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