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).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81e19197-fb52-41db-ac26-ad9c60b1d4c9%2F1350c641-4327-480a-9ec0-e05d0541bdd6%2F83q9jzk_processed.png&w=3840&q=75)
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
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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