Show that the value of sin (x²) dx cannot possibly be 2. Choose the correct answer below. O A. The minimum value of sin (x²) on the interval [0, 1] is greater than 2. Therefore, 1 [sin (x²) dx> [2dx = 2. B. Since sin x is a transcendental function, the value of the integral of sin (x²) irrational number. over [0, 1] must be an OC. The maximum value of sin (x²) on the interval [0, 1] is less than 1. Therefore, 1 1 sin (x²) dxs [1dx=1<2. 0 OD. Since sin x has an average value of 0, the value of the integral of sin (x²) over [0, 1] must be close to 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Show that the value of
S
sin (x²) dx cannot possibly be 2.
0
Choose the correct answer below.
O A. The minimum value of sin (x²) on the interval [0, 1] is greater than 2. Therefore,
1
1
S sin (x²) dx > √2dx = 2.
0
OB. Since sin x is a transcendental function, the value of the integral of sin (x²) over [0, 1] must be an
irrational number.
OC. The maximum value of sin (x²) on the interval [0, 1] is less than 1. Therefore,
1
1
[sin (x²) dx≤ [1dx=1<2.
0
0
Since sin x has an average value of 0, the value of the integral of sin (x²)
over [0, 1] must be close to 0.
Transcribed Image Text:Show that the value of S sin (x²) dx cannot possibly be 2. 0 Choose the correct answer below. O A. The minimum value of sin (x²) on the interval [0, 1] is greater than 2. Therefore, 1 1 S sin (x²) dx > √2dx = 2. 0 OB. Since sin x is a transcendental function, the value of the integral of sin (x²) over [0, 1] must be an irrational number. OC. The maximum value of sin (x²) on the interval [0, 1] is less than 1. Therefore, 1 1 [sin (x²) dx≤ [1dx=1<2. 0 0 Since sin x has an average value of 0, the value of the integral of sin (x²) over [0, 1] must be close to 0.
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