Definite Integral Calculator Problem

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SUMMARY

The discussion revolves around the discrepancy in results when calculating the definite integral 4π∫{0,3/2}(x^3)dx using different calculators. The user, Isaac, correctly computes the integral by hand and with a TI-89, yielding the result of 81π/16. However, both the TI-36X Pro and an online calculator return an incorrect result of 5π/16. The consensus is that the initial calculation is accurate, and the calculators are not at fault.

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  • Understanding of definite integrals in calculus
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poiboi86
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Hi.

Homework Statement



I'm solving the definite integral 4π∫{0,3/2}(x^3)dx

For some reason I get a different answer solving by hand and using my TI-89 than I do when I use an online calculator or my TI-36X Pro. I have to use the TI-36X Pro to take my Engineering FE exam in 2 & 1/2 weeks and need to know why I'm getting these different answers.

Does anyone see what I'm missing?

The Attempt at a Solution



Solving by hand I get πx^4|{0,3/2} = π(3/2)^4 - 0 = 81π/16

This is also what the solution shows, and what my TI-89 calculator gives me as an answer.
But for some reason when I type that same integral into my TI-36X Pro calculator, or an online integral calculator like: <http://www.solvemymath.com/online_math_calculator/calculus/definite_integral/index.php>
I get the answer 15.904 which is 5π/16.


Thank you very much!
Isaac
 
Last edited by a moderator:
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The first answer is correct. 81π/16=15.90431. 5π/16=0.98174. I don't think there is anything wrong the calculators.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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