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1
Calculus: Concepts and Contexts
Find the most general antiderivative of each of the following functions. EXAMPLE
1 (a) (b) (c) , n 1 fx xn fx 1x fx sin x SOLUTION (a) If , then , so an antiderivative of
is . By Theorem 1, the most general antiderivative is . Gx cos x C cos x sin x Fx ...
2
Calculus: Early Transcendentals
Theorem 1 then tells us that the general antiderivative of is on any interval that
doesn't contain 0. In particular, this is true on each of the intervals and . So the
general antiderivative of is x 0 f x 1x f 0, , 0 ln x C Fx lnxC1 lnx C2 ifx0 ifx0 (c) We
use ...
3
Single Variable Calculus: Concepts and Contexts
Find the most general antiderivative of each of the following functions. (a) (b) (c) ,
n 1 fx xn fx 1x fx sin x EXAMPLE 1 SOLUTION (a) If , then , so an antiderivative of
is . By Theorem 1, the most general antiderivative is . Gx cos x C cos x sin x Fx ...
4
Calculus with Analytic Geometry
SECTION 4.11 ANTIDERIVATIVES POLYNOMIAL ANTIDERIVATIVE RULE Let p
(x) be the polynomial Then the antiderivative of p(x), denoted P(x), is „n + 1 - - ' \**
f — "n , i ' ' П+ l where c is a number which may have any value. x* ...
Murray H. Protter, Philip E. Protter, 1988
5
Essential Calculus, Enhanced Edition
If such a function F exists, it is called an antiderivative of f. DEFINITION A function
is called an antiderivative of on an interval if for all in . Ix Fx fx I f F For instance, let
fx x2 . It isn't difficult to discover an antiderivative of if we f keep the Power Rule ...
6
Handbook Of Industrial Automation
4.3 ANTIDERIVATIVES AND INTEGRATION 4.3.1 Antiderivatives One can think
of the antiderivative of a given function as a kind of inverse to the operation of
differentiation, which we saw in Sec. 4.2. This notion is motivated by the so-called
...
Hence —l/3x3 is an antiderivative of l/x“, say for x > O, as also is —(1 /3x3) + c for
any constant c. The table of antiderivatives may be extended to any integer
power of x. An antiderivative of x", for any positive or negative integer n except n I
—l, ...
8
Calculus & Ordinary Differential Equations
Hence —1/3x3 is an antiderivative of l/x“, say for x > O, as also is —(1/3x3) + c for
any constant c. The table of antiderivatives may be extended to any integer
power of x. An antiderivative of x", for any positive or negative integer n except n I
—l, ...
9
The Real Numbers and Real Analysis
Unfortunately, although the concept of an antiderivative is simple to define in
principle, in practice it is not always easy to compute antiderivatives of
complicated functions. Moreover, as we saw in Example 4.4.11, not every
function has an ...
10
Calculus Concepts: An Informal Approach to the Mathematics ...
Designed for a one or two-semester Applied Calculus course, this innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel spreadsheets to help students ...
Donald R. LaTorre, John W. Kenelly, Iris B. Reed, 2011
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «ANTIDERIVATIVE»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
antiderivative w wiadomościach.
I learned more from summer camp than school.
... energy (KE=0.5mv2), what an antithesis is (the contrasting of ideas), how to take the antiderivative of 3×2 (6x) or that 60 Senators are needed ... «Inklings News, Cze 15»
Should I Go To My High School Reunion? Eventbrite's Survey …
After all those nightmares about our teachers discovering we don't remember the Gettysburg Address or how to take an antiderivative, the people who bullied us ... «Bustle, Cze 15»
Business Rallies to Shape Finance Endgame
Goldman denied it, but the charge hardened antibank, anti-Wall Street, antiderivative sentiment in Congress. Corporate treasurers marshaled ... «Wall Street Journal, Cze 10»
