Q21: Select the incorrect step while calculating definite integral ₁³(x² + e-x) dx as limit of sums. < I: f(x) = x² +ex, a = 1, b = 3, h = 2 n II: ₁³(x² + e-x) dx = 2 lim ²½ [ƒ(1) + ƒ (1 + ²) + ƒ (1 + ²) + ... + 1(1+²(n-1))] n18 III: ₁³(x² + e-x) dx = 2 lim ²/ [(1 + e−¹ ) + {(1¹ + ² ) ² + e¯(1¹ + ²)} + {(₁ + ²)² + 6 (¹+)} + + {(1 + ²(x-¹)² + 6 (¹+²+ ²)}]- n-∞ n 2 2 (n- 2(n-1 ... n C n 2 n-∞ IV: S₁³ (x² + e¯x) dx = 2 _lim ²/[(1 + (1 + ²)² + (1 + 3)² + ... + (1 + ²(n−¹)²³) + {e−¹ + e¯(¹+²) + e-(1¹+ ²2 ) + + 0 =(₁+²+ + ²)}} 2(n-1) 2(n- n V: S₁ (x² + e^x) dx = 2 lim :((-) + (7) 1 (1-(1+²) e-1 (1-e n-∞ 1−(1+²) 1-e-(1+1) (a) Only V (b) Only IV (c) Both IV and V (d) All are correct GO Đ
Q21: Select the incorrect step while calculating definite integral ₁³(x² + e-x) dx as limit of sums. < I: f(x) = x² +ex, a = 1, b = 3, h = 2 n II: ₁³(x² + e-x) dx = 2 lim ²½ [ƒ(1) + ƒ (1 + ²) + ƒ (1 + ²) + ... + 1(1+²(n-1))] n18 III: ₁³(x² + e-x) dx = 2 lim ²/ [(1 + e−¹ ) + {(1¹ + ² ) ² + e¯(1¹ + ²)} + {(₁ + ²)² + 6 (¹+)} + + {(1 + ²(x-¹)² + 6 (¹+²+ ²)}]- n-∞ n 2 2 (n- 2(n-1 ... n C n 2 n-∞ IV: S₁³ (x² + e¯x) dx = 2 _lim ²/[(1 + (1 + ²)² + (1 + 3)² + ... + (1 + ²(n−¹)²³) + {e−¹ + e¯(¹+²) + e-(1¹+ ²2 ) + + 0 =(₁+²+ + ²)}} 2(n-1) 2(n- n V: S₁ (x² + e^x) dx = 2 lim :((-) + (7) 1 (1-(1+²) e-1 (1-e n-∞ 1−(1+²) 1-e-(1+1) (a) Only V (b) Only IV (c) Both IV and V (d) All are correct GO Đ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve in20 min properly
![13:19 18
x
Q21: Select the incorrect step while calculating definite integral
₁³(x² + e-x) dx as limit of sums.
I: f(x) = x² + e*, a = 1, b = 3, h
=
E
n
+ ... +
n-8
II: ₁³(x² + e-x) dx = 2 lim [ƒ(1) + ƒ (1 + ²) + ƒ (1 + ²) +
f(1+23)]
IV: f'(x² + e) dx = 2 lim
n→∞ n
2
III: (x² + e^²) dx = 2 lim [(1¹ + e^²¹) + { ( ¹ + ²)² + e-¯( ¹ + ² } +
{(1
2
n-∞ n
e−(¹
{ ( 1 + ² ) ²³ + e ¯( ¹ + ²) } + ... + {(1₁ + - ² (n-1))².
e^(1+5
(a) Only V
(b) Only IV
(c) Both IV and V
(d) All are correct
Vol)
LTE2
V: f(x² + e-x) dx = 2 lim 1/2
n-∞ n
{[(
(1 + ²(n-¹) ²) + {e-¹ + e¯(¹+²³) + e - (¹ +²3)
e−(¹ + ... + e
2)
1
²/ [(1
(¹ + ( ₁ + ² + ( ¹ + ² + - +
(1 ²)² (1 ²)²
...
) +
2(n-1)
1-(1 + ²)²
1−(1+²)
n
+2)}] ²
87%
· + e^(1+² (n-1)
+ D) } ]
n
e-¹ (1-e¯(¹+/-)n)
1-e-(1+)
CO
←
G](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffac8583b-e586-4d83-bc0b-917d911d0e04%2F58ce83b2-e40d-4d13-8095-8061a48c284c%2F28148ro_processed.jpeg&w=3840&q=75)
Transcribed Image Text:13:19 18
x
Q21: Select the incorrect step while calculating definite integral
₁³(x² + e-x) dx as limit of sums.
I: f(x) = x² + e*, a = 1, b = 3, h
=
E
n
+ ... +
n-8
II: ₁³(x² + e-x) dx = 2 lim [ƒ(1) + ƒ (1 + ²) + ƒ (1 + ²) +
f(1+23)]
IV: f'(x² + e) dx = 2 lim
n→∞ n
2
III: (x² + e^²) dx = 2 lim [(1¹ + e^²¹) + { ( ¹ + ²)² + e-¯( ¹ + ² } +
{(1
2
n-∞ n
e−(¹
{ ( 1 + ² ) ²³ + e ¯( ¹ + ²) } + ... + {(1₁ + - ² (n-1))².
e^(1+5
(a) Only V
(b) Only IV
(c) Both IV and V
(d) All are correct
Vol)
LTE2
V: f(x² + e-x) dx = 2 lim 1/2
n-∞ n
{[(
(1 + ²(n-¹) ²) + {e-¹ + e¯(¹+²³) + e - (¹ +²3)
e−(¹ + ... + e
2)
1
²/ [(1
(¹ + ( ₁ + ² + ( ¹ + ² + - +
(1 ²)² (1 ²)²
...
) +
2(n-1)
1-(1 + ²)²
1−(1+²)
n
+2)}] ²
87%
· + e^(1+² (n-1)
+ D) } ]
n
e-¹ (1-e¯(¹+/-)n)
1-e-(1+)
CO
←
G
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