Hello,tmt said:Hi,
When integrating this function, "y=ax^n"
the answer is "(ax^n)/(n+1) + C", correct?
Thank you,
Tim
The formula for the integral of ax^n is ∫ax^n dx = a/(n+1)x^(n+1) + C, where C is the constant of integration.
The power rule for integration states that the integral of x^n dx is equal to x^(n+1) / (n+1) + C.
To solve a definite integral with ax^n, you can use the formula ∫ax^n dx = a/(n+1)x^(n+1) + C and substitute the limits of integration into the equation. Then, subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the final result.
Yes, the integral of ax^n can be solved using substitution. However, it is important to choose the substitution carefully in order to simplify the integral and make it easier to solve.
The derivative of ax^n is equal to a*n*x^(n-1), while the integral of ax^n is equal to a/(n+1)x^(n+1) + C. Therefore, the integral of ax^n is the antiderivative of the derivative of ax^n.