(a) Use a computer algebra system to evaluate the following integrals. 1 (1) dx (ii) (x+2)(x+3) (x + 1)(x + 5) 1 (iii) (iv) (x + 2)² dx (b) Based on the pattern of your responses in part (a). guess the value of the integral 1 (x+2)(x-5) dx (x + a)(x + b) dx dx if ab. What if ab? (c) Check your guess by asking your CAS to evaluate the integral in part (b). Then prove it using partial fractions.
(a) Use a computer algebra system to evaluate the following integrals. 1 (1) dx (ii) (x+2)(x+3) (x + 1)(x + 5) 1 (iii) (iv) (x + 2)² dx (b) Based on the pattern of your responses in part (a). guess the value of the integral 1 (x+2)(x-5) dx (x + a)(x + b) dx dx if ab. What if ab? (c) Check your guess by asking your CAS to evaluate the integral in part (b). Then prove it using partial fractions.
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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![1. (a) Use a computer algebra system to evaluate the following integrals.
1
(1)
(ii)
(x + 2)(x+3)
1
- dx
1
(x + 1)(x + 5)
1
]x+2
(x + 2)²
(ii)(x+2)(x - 5) dx
(iv)
(b) Based on the pattern of your responses in part (a), guess the value of the integral
1
√ √(x + a)(x + b) "
dx
dx
dx
if ab. What if a = b?
*
(c) Check your guess by asking your CAS to evaluate the integral in part (b). Then prove it
using partial fractions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6caac49-b571-4d61-a050-647f9235352a%2F9e954589-e569-46af-b13c-933aecfb62c5%2Fylb0soa_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Use a computer algebra system to evaluate the following integrals.
1
(1)
(ii)
(x + 2)(x+3)
1
- dx
1
(x + 1)(x + 5)
1
]x+2
(x + 2)²
(ii)(x+2)(x - 5) dx
(iv)
(b) Based on the pattern of your responses in part (a), guess the value of the integral
1
√ √(x + a)(x + b) "
dx
dx
dx
if ab. What if a = b?
*
(c) Check your guess by asking your CAS to evaluate the integral in part (b). Then prove it
using partial fractions.
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