Editing 1201: Integration by Parts
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The title text points out that if the integral of x can be divided so that u = x and dv = dx and implying v = x, then it leads to the result (1/2)x². This implies the original integral was just ∫x dx, and not needing integration by parts in the first place. Mathematics teachers and extreme math geeks will also cringe at this answer, however, since an {{w|indefinite integral}} requires an integration constant. The correct answer is actually (1/2)x² + C, as Randall hints. The +C symbolizes that an indefinite integral can be shifted by any constant and still gets the same answer on the reverse {{w|derivative}}. {{w|Integral|Definite integrals}} specify a range that they're valid on and thus there is no need to add this constant. | The title text points out that if the integral of x can be divided so that u = x and dv = dx and implying v = x, then it leads to the result (1/2)x². This implies the original integral was just ∫x dx, and not needing integration by parts in the first place. Mathematics teachers and extreme math geeks will also cringe at this answer, however, since an {{w|indefinite integral}} requires an integration constant. The correct answer is actually (1/2)x² + C, as Randall hints. The +C symbolizes that an indefinite integral can be shifted by any constant and still gets the same answer on the reverse {{w|derivative}}. {{w|Integral|Definite integrals}} specify a range that they're valid on and thus there is no need to add this constant. | ||
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+ | [[569: Borders]] makes a subtle reference to integration by parts (the name of the kingdom). | ||
==Transcript== | ==Transcript== |