a a If f is an even function, why is f(x) dx = 2 f(x) dx? Choose the correct answer below. O A. a a a Since f is even, f is symmetric about the origin. Therefore, |f(x) dx = f(x) dx = f(x) dx + f(x) dx = 2 f(x) dx. + xp 0. - a -a 0. a a a a a В. Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx = f(x) dx = | f(x) dx + f(x) dx - f(x) dx = 2 f(x) c a a a a a a OC. f(x) dx = - f(x) dx = f(x) dx + f(x) dx = 2 f(x) dx. Since f is even, f is symmetric about the y-axis. Therefore,

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Related questions
Question
a
If f is an even function, why is
f(x) dx = 2 | f(x) dx?
- a
Choose the correct answer below.
А.
a
a
a
a
a
Since f is even, f is symmetric about the origin. Therefore, f(x) dx = | f(x) dx →
f(x) dx =
| f(x) dx +
f(x) dx
f(x) dx = 2 | f(x) dx.
%3D
- a
- a
- a
- a
a
a
a
a
a
O B.
Since fis even, fis symmetric about the y-axis. Therefore, S 10) dk = [tox) dx → [ to0) dx = [ tx) dx + [rtx) dx → S t0) dk=2[1w) cx
Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx = | f(x) dx →
f(x) dx +
f(x) dx –
f(x) dx = 2 | f(x) dx.
- a
- a
- a
- a
a
a
- Joma - Jwar Jma foma- jwarafma
С.
f(x) dx →
| f(x) dx =
f(x) dx + | f(x) dx →
f(x) dx = 2 | f(x) dx.
%3D
Since f is even, f is symmetric about the y-axis. Therefore, | f(x) dx =
- a
Transcribed Image Text:a If f is an even function, why is f(x) dx = 2 | f(x) dx? - a Choose the correct answer below. А. a a a a a Since f is even, f is symmetric about the origin. Therefore, f(x) dx = | f(x) dx → f(x) dx = | f(x) dx + f(x) dx f(x) dx = 2 | f(x) dx. %3D - a - a - a - a a a a a a O B. Since fis even, fis symmetric about the y-axis. Therefore, S 10) dk = [tox) dx → [ to0) dx = [ tx) dx + [rtx) dx → S t0) dk=2[1w) cx Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx = | f(x) dx → f(x) dx + f(x) dx – f(x) dx = 2 | f(x) dx. - a - a - a - a a a - Joma - Jwar Jma foma- jwarafma С. f(x) dx → | f(x) dx = f(x) dx + | f(x) dx → f(x) dx = 2 | f(x) dx. %3D Since f is even, f is symmetric about the y-axis. Therefore, | f(x) dx = - a
a
a
Iff is an even function, why is
f(x) dx = 2 f(x) dx?
- a
J
J
J
J
- a
- a
a
- a
O B.
0.
a
a
a
a
a
Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx = | f(x) dx →
| f(x) dx =
|f(x) dx +
f(x) dx →
| f(x) dx = 2 | f(x) dx.
- a
- a
- a
- a
С.
a
a
a
a
a
Since f is even, f is symmetric about the y-axis. Therefore,
f(x) dx →
f(x) dx =
f(x) dx + | f(x) dx →
| f(x) dx = 2 | f(x) dx.
%3D
- a
- a
- a
- a
D.
a
a
a
a
Since f is even, f is symmetric about the origin. Therefore, f(x) dx= - | f(x) dx →
f(x) dx =
| f(x) dx + f(x) dx →
| f(x) dx = 2 f(x) dx.
- a
- a
- a
- a
Transcribed Image Text:a a Iff is an even function, why is f(x) dx = 2 f(x) dx? - a J J J J - a - a a - a O B. 0. a a a a a Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx = | f(x) dx → | f(x) dx = |f(x) dx + f(x) dx → | f(x) dx = 2 | f(x) dx. - a - a - a - a С. a a a a a Since f is even, f is symmetric about the y-axis. Therefore, f(x) dx → f(x) dx = f(x) dx + | f(x) dx → | f(x) dx = 2 | f(x) dx. %3D - a - a - a - a D. a a a a Since f is even, f is symmetric about the origin. Therefore, f(x) dx= - | f(x) dx → f(x) dx = | f(x) dx + f(x) dx → | f(x) dx = 2 f(x) dx. - a - a - a - a
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