Which of the following is equivalent to (A) (B C (D L² (x5 - - 4x + 6) dx [² (2³-42) (x5 - 4x³+6) dx ²22²-42³² +68 x7 x² - L₁² (2₂.5. (x5 - 4x + 6x-2) dx ₁² (2²7-42³ +62-²) da -dx?
Which of the following is equivalent to (A) (B C (D L² (x5 - - 4x + 6) dx [² (2³-42) (x5 - 4x³+6) dx ²22²-42³² +68 x7 x² - L₁² (2₂.5. (x5 - 4x + 6x-2) dx ₁² (2²7-42³ +62-²) da -dx?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem:**
Which of the following is equivalent to
\[
\int_{1}^{2} \frac{x^7 - 4x^3 + 6}{x^2} \, dx \, ?
\]
**Options:**
A. \(\int_{1}^{2} (x^5 - 4x + 6) \, dx\)
B. \(\int_{1}^{2} (x^5 - 4x^3 + 6) \, dx\)
C. \(\int_{1}^{2} (x^5 - 4x + 6x^{-2}) \, dx\)
D. \(\int_{1}^{2} (x^7 - 4x^3 + 6x^{-2}) \, dx\)
**Explanation:**
The expression
\(\frac{x^7 - 4x^3 + 6}{x^2}\)
can be simplified by dividing each term in the numerator by \(x^2\):
- \(x^7/x^2 = x^5\)
- \(-4x^3/x^2 = -4x\)
- \(6/x^2 = 6x^{-2}\)
Thus, the simplified integral is:
\(\int_{1}^{2} (x^5 - 4x + 6x^{-2}) \, dx\)
Therefore, the correct option is **C**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F019fb4ae-aebc-4c9c-a0ae-00e747a06944%2Fe42cdc56-85e9-489a-b2bf-08a060a8860d%2Fgqmuq9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Which of the following is equivalent to
\[
\int_{1}^{2} \frac{x^7 - 4x^3 + 6}{x^2} \, dx \, ?
\]
**Options:**
A. \(\int_{1}^{2} (x^5 - 4x + 6) \, dx\)
B. \(\int_{1}^{2} (x^5 - 4x^3 + 6) \, dx\)
C. \(\int_{1}^{2} (x^5 - 4x + 6x^{-2}) \, dx\)
D. \(\int_{1}^{2} (x^7 - 4x^3 + 6x^{-2}) \, dx\)
**Explanation:**
The expression
\(\frac{x^7 - 4x^3 + 6}{x^2}\)
can be simplified by dividing each term in the numerator by \(x^2\):
- \(x^7/x^2 = x^5\)
- \(-4x^3/x^2 = -4x\)
- \(6/x^2 = 6x^{-2}\)
Thus, the simplified integral is:
\(\int_{1}^{2} (x^5 - 4x + 6x^{-2}) \, dx\)
Therefore, the correct option is **C**.
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