15 f(æ)dæ f(x)dx where a = and b
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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![The image contains an equation involving definite integrals and requires determining unspecified limits of integration for a function \( f(x) \).
### Equation:
\[
\int_{3}^{15} f(x) \, dx - \int_{3}^{6} f(x) \, dx = \int_{a}^{b} f(x) \, dx
\]
### Explanation:
- The expression on the left involves two integrals with limits from 3 to 15 and from 3 to 6.
- The subtraction of these integrals suggests finding the integral from 6 to 15.
- The right side of the equation is a definite integral from \( a \) to \( b \) of the same function \( f(x) \).
### Task:
Fill in the placeholders for \( a \) and \( b \) below the equation:
- **where \( a = \)**
- **and \( b = \)**
In this context, solving the equation involves determining the values of \( a \) and \( b \) such that the integral from \( a \) to \( b \) equals the integral from 6 to 15.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bb7c04b-31f7-4ac4-b04e-9c07278fceb0%2F4e701218-d5e7-4c78-bfec-ad409464fbb3%2Fkdm1amj_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains an equation involving definite integrals and requires determining unspecified limits of integration for a function \( f(x) \).
### Equation:
\[
\int_{3}^{15} f(x) \, dx - \int_{3}^{6} f(x) \, dx = \int_{a}^{b} f(x) \, dx
\]
### Explanation:
- The expression on the left involves two integrals with limits from 3 to 15 and from 3 to 6.
- The subtraction of these integrals suggests finding the integral from 6 to 15.
- The right side of the equation is a definite integral from \( a \) to \( b \) of the same function \( f(x) \).
### Task:
Fill in the placeholders for \( a \) and \( b \) below the equation:
- **where \( a = \)**
- **and \( b = \)**
In this context, solving the equation involves determining the values of \( a \) and \( b \) such that the integral from \( a \) to \( b \) equals the integral from 6 to 15.
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