MHB Is \(\frac{ax^n}{n+1} + C\) the Correct Integral of \(y=ax^n\)?

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The integral of the function \(y=ax^n\) is correctly expressed as \(\frac{ax^{n+1}}{n+1} + C\). The initial assumption that the integral is \(\frac{ax^n}{n+1} + C\) is incorrect. The integration must be performed with respect to \(x\), which leads to the increase in the exponent. This clarification emphasizes the importance of proper integration techniques. Understanding these fundamentals is crucial for accurate calculus applications.
tmt1
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Hi,

When integrating this function $y=a x^n $

the answer is $$\frac{ax^n}{n+1} + C$$ , correct?

Thank you,

Tim
 
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tmt said:
Hi,

When integrating this function, "y=ax^n"

the answer is "(ax^n)/(n+1) + C", correct?

Thank you,

Tim
Hello,
The correct answer is $$\frac{ax^{n+1}}{n+1}+c$$ can you see WHY?
I asume that we integrate respect to x!

Regards,
$$|\pi\rangle$$
 
Excellent, thank you!
 
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