inte b-a [*1 (x) dx f (x) dx = limf (x;) A.x, where Ax = Δ., 71-00 Use the given form of the definition to evaluate the integral. n

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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5.2 q9

Tutorial Exercise
If f is integrable on [a, b], the following equation is correct.
[²ƒ (x) dx =
=
Part 1 of 6
Part 2 of 6
i=1
Use the given form of the definition to evaluate the integral.
La
Part 3 of 6
Using
6i
If Xo = -2, then each x; = −2+ iAx = -2 +
lim
72-00
Since the interval is [-2, 4] and we have n sub-intervals, then Ax =
Part 4 of 6
(1 + 5x) dx
n
Now, lim
72
i=1
lim Ĺ (1 + 5(-2 + 6i)) 6 =
Σ
77-00
i = 1
4
12 (1 + 5x) dx = lim (1 + 5x;) Ax, we have
n→∞o
f (xi) Ax, where A.x =
n-coin
Σ=1
i = 1
n
6
- -º- (-9 + 301) =
n
i = 1
X
n
· = lim £Σ (Ε
n
6
= lim
n→∞ n
Submit Skip (you cannot come back)
^6-3
i = 1
i=1
-9 +
b- a
n
n
n
6i
and x₂ =
+
30i
But
M³
= a +iAx.
n
n
30i
-9 = 36
6
X
"
and
Transcribed Image Text:Tutorial Exercise If f is integrable on [a, b], the following equation is correct. [²ƒ (x) dx = = Part 1 of 6 Part 2 of 6 i=1 Use the given form of the definition to evaluate the integral. La Part 3 of 6 Using 6i If Xo = -2, then each x; = −2+ iAx = -2 + lim 72-00 Since the interval is [-2, 4] and we have n sub-intervals, then Ax = Part 4 of 6 (1 + 5x) dx n Now, lim 72 i=1 lim Ĺ (1 + 5(-2 + 6i)) 6 = Σ 77-00 i = 1 4 12 (1 + 5x) dx = lim (1 + 5x;) Ax, we have n→∞o f (xi) Ax, where A.x = n-coin Σ=1 i = 1 n 6 - -º- (-9 + 301) = n i = 1 X n · = lim £Σ (Ε n 6 = lim n→∞ n Submit Skip (you cannot come back) ^6-3 i = 1 i=1 -9 + b- a n n n 6i and x₂ = + 30i But M³ = a +iAx. n n 30i -9 = 36 6 X " and
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