ind So Can the Fundamental Theorem of Calculus be used to find 2 2x²-x-3 dx? 2x²- √x O No, f(x) = ² 2x²-x-3 dx is not continuous on the given interval and i T
ind So Can the Fundamental Theorem of Calculus be used to find 2 2x²-x-3 dx? 2x²- √x O No, f(x) = ² 2x²-x-3 dx is not continuous on the given interval and i T
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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![### Can the Fundamental Theorem of Calculus be used to find
\[ \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx? \]
1. ◯ No, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is not continuous on the given interval and its antiderivative does not exist.
2. ◯ Yes, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is continuous on the given interval and its antiderivative exists.
3. ◯ Yes, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is continuous on the given interval but its antiderivative does not exist.
4. ◉ No, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is not continuous on the given interval but its antiderivative exists.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8332b21a-7711-4793-b2df-7a1f1091dd0f%2Ffc78a626-0d03-4511-921b-804268860bd3%2Fm1mi09j_processed.png&w=3840&q=75)
Transcribed Image Text:### Can the Fundamental Theorem of Calculus be used to find
\[ \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx? \]
1. ◯ No, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is not continuous on the given interval and its antiderivative does not exist.
2. ◯ Yes, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is continuous on the given interval and its antiderivative exists.
3. ◯ Yes, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is continuous on the given interval but its antiderivative does not exist.
4. ◉ No, \( f(x) = \int_{0}^{2} \frac{2x^2 - x - 3}{\sqrt{x}} \, dx \) is not continuous on the given interval but its antiderivative exists.
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