Evaluate the definite integral by the limit definition. Step 1 J4 5 dx To find the definite integral 5 dx by the limit definition, divide the interval [4, 9] into n subintervals. Step 2 Then the width of each interval is b-a Ax = Note that ||A||- → n J4 5 n 9-4 n O as n→ 00.
Evaluate the definite integral by the limit definition. Step 1 J4 5 dx To find the definite integral 5 dx by the limit definition, divide the interval [4, 9] into n subintervals. Step 2 Then the width of each interval is b-a Ax = Note that ||A||- → n J4 5 n 9-4 n O as n→ 00.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 17E
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Question
![Evaluate the definite integral by the limit definition.
[²5
Step 1
5 dx
To find the definite integral
Then the width of each interval is
b-a
Ax =
Note that ||A||
→
n
=
=
Step 2
Choose c; as the right endpoint of each subinterval. Then
C₁ = a + i(Ax) =
So the definite integral is given by
=
=
5
=
n
[²5 dx = lim Σκ(c;) Δx
IAI → 0
i = 1
=
=
n→
[²
5 dx by the limit definition, divide the interval [4, 9] into n subintervals.
lim
n→ ∞
n
n→
lim Σ
n→∞
i = 1
n→
lim
n→∞0
O as n→→ ∞0.
lim
i = 1
lim
lim
n→ ∞ n
94
lim
25.
+i
A
i = 1
1
f(c;) Ax
+
n
(5)
1
n
n
i = 1
1)()
25](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba58da1-aa6c-4b34-ac65-53856b97f0bf%2F5d27609b-05b2-40f3-86d9-62d6ddc887ae%2Fnw515qv_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate the definite integral by the limit definition.
[²5
Step 1
5 dx
To find the definite integral
Then the width of each interval is
b-a
Ax =
Note that ||A||
→
n
=
=
Step 2
Choose c; as the right endpoint of each subinterval. Then
C₁ = a + i(Ax) =
So the definite integral is given by
=
=
5
=
n
[²5 dx = lim Σκ(c;) Δx
IAI → 0
i = 1
=
=
n→
[²
5 dx by the limit definition, divide the interval [4, 9] into n subintervals.
lim
n→ ∞
n
n→
lim Σ
n→∞
i = 1
n→
lim
n→∞0
O as n→→ ∞0.
lim
i = 1
lim
lim
n→ ∞ n
94
lim
25.
+i
A
i = 1
1
f(c;) Ax
+
n
(5)
1
n
n
i = 1
1)()
25
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