How to Use the Power Rule of Integration in Calculus


The power rule of integration gives you the general solution for the integral of any variable raised to any power except -1, which represents a special case. Since integrals are antiderivatives -- in other words, if you integrate the derivative of a function, you end up with the original function -- think of the power rule of integration as doing the opposite of what the power rule for derivatives does.

Things You'll Need

  • Paper
  • Pencil
  • Convert any square roots, roots of other powers and powers in denominators to standard power functions. The square root of x equals x^(1/2), the cube root of x equals x^(1/3) and so on for the other roots. To move a power from the denominator to the numerator, take the inverse of the power: 1/x^2 = x^-2, for example.

  • Add one to the power. For int[(x^3)dx], for example, x^3 becomes x^4.

  • Divide the result by the new power. For example, x^4 becomes (x^4)/4.

  • Add the constant of integration, usually represented by c, to complete your answer. For example, [(x^4)/4] + c.

Tips & Warnings

  • To integrate a constant, think of the constant as being multiplied by x^0. For example, int(2 dx) = int[(2x^0)dx] = (2x^1)/1 + c = 2x + c.
  • If the integral includes addition or subtraction, integrate each part of the function separately; think of int[(x + 2)dx] as int(x dx) + int (2 dx), for example.
  • The integral of 1/x, or x^-1, equals ln|x| + c.
  • When working with negative exponents, remember that adding one will make the absolute value of the exponent smaller; x^-3 becomes x^-2, not x^-4.


Promoted By Zergnet


You May Also Like

  • The Power Rule of Calculus

    How to Use the Power Rule of Integration in Calculus. How to Differentiate the Function in Calculus. How to Apply the Constant...

  • What Is "Double Integration" in Calculus?

    How to Use the Power Rule of Integration in Calculus. Who Invented Calculus? Featured. Top 10 Produce to Eat. View Photos. Make...

  • How to Integrate Exponents

    How to Integrate Exponents. The general rule for integrating exponential terms consists of three steps: ... How to Integrate Power & Polynomial...

  • Structure & Organization of Plants

    The structure and organization of the plants you're attempting to grow is integral to the success of a garden. Learn about the...

  • The Integration of Algebraic Functions

    The Integration of Algebraic Functions. Part of the series: Algebra Tips. ... but the rule for the power rule is you take...

  • Continuity Rules of Calculus

    What Is "Double Integration" in Calculus? Problems With Half-Life in Calculus. ... Differences Between the Power Rule & the Chain Rule in...

Related Searches

Read Article

Can You Take Advantage Of Student Loan Forgiveness?

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!