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The mathematics displayed is neither {{w|semantically}} nor {{w|syntactically}} correct. To begin with, there should (reasonably) be a ''dx'' after x<sup>2</sup>. Adding this, we have an {{w|indefinite integral}} on the left hand side. | The mathematics displayed is neither {{w|semantically}} nor {{w|syntactically}} correct. To begin with, there should (reasonably) be a ''dx'' after x<sup>2</sup>. Adding this, we have an {{w|indefinite integral}} on the left hand side. | ||
| − | The answer | + | The answer {{w|π}} is just nonsensical: What we want is a {{w|Function (mathematics)|function}} whose {{w|derivative}} is x<sup>2</sup>. Now, x<sup>3</sup>/3 satisfies this condition. However, since adding a {{w|constant (mathematics)|constant}} to a function does not change its derivative, the full answer is (any function of the form) x<sup>3</sup>/3 {{w|Constant of integration|+ C}}, where C is any fixed number. The "plus a constant" part is very easy to forget, and might even be omitted by a (sloppy) professional mathematician. So if someone really gave the answer π, "you forgot to add a constant" would be a pretty funny remark, because in one way it's true, but on the other hand it wouldn't quite be the main thing to worry about. (It is especially inane as π itself ''is'' a constant.) |
It would also be possible to fix the equation by adding [http://www.mathwords.com/b/bounds_of_integration.htm bounds of integration], so that {{w|π}} becomes the area below a section of the curve x<sup>2</sup>. That is called a definite integral, and there would be no "+ C". The bounds would have to be somewhat awkward though; if 0 was the lower bound, the cube root of 3π would have to be the upper. | It would also be possible to fix the equation by adding [http://www.mathwords.com/b/bounds_of_integration.htm bounds of integration], so that {{w|π}} becomes the area below a section of the curve x<sup>2</sup>. That is called a definite integral, and there would be no "+ C". The bounds would have to be somewhat awkward though; if 0 was the lower bound, the cube root of 3π would have to be the upper. | ||
