Undergrad Why Is the Integral Result 175/3 Instead of 45?

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The integral of y, expressed as (1/3)x^3 + 2x, evaluated from the upper limit of 5 to the lower limit of 2, yields a result of 45, not 175/3. The correct evaluation of 175/3 occurs if the lower limit is set at x=-2. Participants suspect a possible typo or calculation error by the question setter. Additionally, there is a notation clarification suggesting that (1/3)x^3 should be used to avoid confusion with 1/(3x^3). This discussion highlights the importance of precise notation in mathematical expressions.
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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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homeworkhelpls said:
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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
Both Wolfram Alpha and I agree with you.
 
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Me too!
 
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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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homeworkhelpls said:
View attachment 321610
i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
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.
 

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