integrate negative power variableexplain how to integrate negative power variable

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to consider the following function hence, integrating the function yields:

You may substitute any value for n, this does not affect the way you evaluate the integral.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll integrate the negative power as we do when integrate positive powers.

Supposing that we'll have the function f(x) = 1/x^3.

We'll integrate f(x):

Int f(x)dx = Int dx/x^3

We do not know to integrate the expression above, so we'll

apply the following rule:

x^-3 = 1/x^3

As we can remark, the negative power moves the base "x", to the denominator.

Int dx/x^3  = Int x^-3dx

We know now to integrate the power function:

Int x^n dx = x^(n+1)/(n+1) + C

Comparing, we'll get:

Int x^-3dx = x^(-3+1)/(-3+1) + C

Int x^-3dx = x^-2/-2 + C

Int x^-3dx = -1/2x^2 + C

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