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

  • Context: MHB 
  • Thread starter Thread starter tmt1
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
SUMMARY

The correct integral of the function \(y=ax^n\) is \(\frac{ax^{n+1}}{n+1} + C\), not \(\frac{ax^n}{n+1} + C\). This conclusion is reached by applying the power rule of integration, which states that when integrating \(x^n\), the exponent is increased by one and divided by the new exponent. The discussion emphasizes the importance of integrating with respect to \(x\).

PREREQUISITES
  • Understanding of basic calculus concepts, specifically integration.
  • Familiarity with the power rule of integration.
  • Knowledge of algebraic manipulation of expressions.
  • Ability to differentiate between constants and variables in integration.
NEXT STEPS
  • Study the power rule of integration in detail.
  • Explore examples of integrating polynomial functions.
  • Learn about common mistakes in integration and how to avoid them.
  • Review the concept of indefinite integrals and the role of the constant \(C\).
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone looking to solidify their understanding of polynomial integration.

tmt1
Messages
230
Reaction score
0
Hi,

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

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

Thank you,

Tim
 
Last edited by a moderator:
Physics news on Phys.org
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!
 

Similar threads

Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
  • · Replies 5 ·
Replies
5
Views
3K
High School Some questions regarding the integral of cos(ax), "a" not zero
  • · Replies 17 ·
Replies
17
Views
5K
Undergrad Resolve the Recursion of Dickson polynomials
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Express the limit as a definite integral
  • · Replies 16 ·
Replies
16
Views
4K
MHB Indefinite integral in division form
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Definite integral is undefined and not undefined
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Limit of ##i^\frac{1}{n}## as ##n \to \infty##
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Infinite Series - Divergence of 1/n question
  • · Replies 5 ·
Replies
5
Views
2K
MHB Maximizing $y=|4x^3+ax^2+bx+c|$ in $[-1,1]$
  • · Replies 1 ·
Replies
1
Views
1K
MHB Using advanced calculus for finding values
  • · Replies 2 ·
Replies
2
Views
1K