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homeworkhelpls
- 41
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i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
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Why Is the Integral Result 175/3 Instead of 45?
In summary, the speaker integrated y using the upper limit of 5 and lower limit of 2 in order to get the result of 45/3, but the correct answer should have been 175/3. This discrepancy may be due to a typo or calculation error by the person who set the question. Additionally, using the notation (1/3)x^3 instead of 1/3x^3 can help avoid confusion.
i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
- #2
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Both Wolfram Alpha and I agree with you.homeworkhelpls said:
- #3
Maarten Havinga
- 76
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Me too!
- #4
Ibix
Science Advisor
- 12,568
- 14,689
The integral would evaluate to 175/3 if the lower limit were x=-2. I suspect a silly typo or calculation slip by the question setter.
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- #5
YouAreAwesome
Gold Member
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Just a notation tip. 1/3x^3 can be misread as 1/(3x^3) placing the x^3 in the denominator. To be precise, we can instead write (1/3)x^3 to ensure x^3 is in the numerator and not mistakenly placed in the denominator.homeworkhelpls said:
FAQ: Why Is the Integral Result 175/3 Instead of 45?
What is the integral being evaluated to result in 175/3?
The integral in question typically involves a specific function over a defined interval. Without the exact function and limits, it's challenging to provide a precise answer. However, integrals that yield results like 175/3 often involve polynomial or rational functions that are integrated over a range that captures significant area under the curve.
How do you calculate the integral that results in 175/3?
To calculate the integral, you would first determine the function to be integrated and the limits of integration. You would then apply the fundamental theorem of calculus, which involves finding the antiderivative of the function and evaluating it at the upper and lower limits. The difference between these evaluations will yield the result, which in this case is 175/3.
Why might someone expect the integral result to be 45 instead of 175/3?
The expectation of the result being 45 could stem from a misunderstanding of the function being integrated, the limits of integration, or a miscalculation. It is also possible that the expected result pertains to a different problem or a simplified version of the integral that does not account for all the factors involved.
What are common mistakes that lead to incorrect integral results?
Common mistakes include errors in algebraic manipulation, incorrect application of integration techniques, misidentifying the limits of integration, or failing to account for the properties of the function being integrated. Additionally, overlooking constants or miscalculating definite integrals can lead to discrepancies in results.
How can I verify the integral result of 175/3?
You can verify the integral result by re-evaluating the integral using different methods, such as numerical integration or graphing the function to visually confirm the area under the curve. Additionally, using software tools or calculators that support symbolic computation can help ensure that the calculations are accurate and consistent.