Integration by Substitution (also called u-Substitution or The Reverse Chain Rule) is a method to find an integral, but only when it can be set up in a special way.
The theoretical basis for integration by substitution is the chain rule for differentiation, which says that$$\\frac{d} {{dx}}f(g(x))\\; = f'(g(x))\\;g'(x)$$. Regarding integration as the reverse of differentiation leads us to integrate both sides of this equation to write $$\...
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1 10.1 Integration by Substitution Each basic rule of integration that you have studied so far was derived from a corresponding differentiation rule. Even though you have learned all the necessary tools for differentiating exponential, logarithmic, trigonometric, and algebraic functions, your set of too...
托马斯微积分课件4.2 Intergal Rules; Integration by substitution Chapter4Integration 4.1IndefiniteIntegrals,DifferentialEquations,andModeling4.2IntegralRules,IntegrationbySubstitution4.3EstimatingwithFiniteSums 4.4RiemannSumsandDefiniteIntegrals4.5TheMeanValueandFundamentalTheorems 4.6SubstitutioninDefiniteIntegrals4....
we have ∫f(x) dx = ∫f(v)v' du Example: ∫sqrt(1-x^2) dx Let x=sin u dx/du=cos u =∫sqrt(1-sin^2 u) cos u du =∫cos^2 u du By using double angle formula one more substitution =(sin 2u)/2 + u/2 + C x=sin u u=arcsin x =(sin (2arcsin x))/2...
AP CalculusIntegral——IntegrationbySubstitution2015.12.16 Rules: If , then . If , thenIf , . Evaluate the indefinite integral. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. AP CalculusIntegral——IntegrationbySubstitution2015.12.17 Evaluate the ...
Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with...
integration by substitution 代换积分法 effect of substitution 替代效应 electrophilic substitution 亲电子取代作用 substitution swap 替代掉换系债券掉换(*bond swap)的一种,指为了改善原有债券的一个或数个性质(品质、收益率等),而同时卖出某一证券以买入另一种证券的操作方式。 substitution class phr. n....
by M. Bourne In this section, we see how to integrate expressions like Depending on the function we need to integrate, wesubstituteone of the following trigonometric expressions to simplify the integration: Fora2−x2\displaystyle\sqrt{{{a}^{2}-{x}^{2}}}a2−x2, usex=asinθ\...