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Rules for integrals

Rules for Integrals

  1. Sum rule:The integral of the sum or difference of two functions is the sum or difference of their integrals.MATH

  2. Constant multiple:The integral of a constant times a function is the constant times the integral of the function.MATH

  3. Power rule:The integral of $x^{n}$ is MATH.MATH

  4. Integration by parts:The integral of a product is the first factor times the integral of the second minus the integral of the derivative of the first times the integral of the second.MATH

  5. Fundamental theorem of calculus, first formIf $f$ is continuous on $\left[ a,b\right] $ then the function $g$ defined by MATHis continuous on $\left[ a,b\right] $ and MATH for each $x$ in the open interval $\left( a,b\right) $.

  6. Fundamental theorem of calculus, second formIf $f$ is continuous on $\left[ a,b\right] $ then MATHwhere $F$ is any antiderivative of $f$.

  7. Change of variable for indefinite integralsIf $u=g(x)$ is a differentiable function of $x$, then MATH andMATH


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Rules for derivatives

Rules for limits


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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