Integration Question, help please (1 Viewer)
- Thread starter froglenn
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Froglenn, Affinity is right, and so int x<sup>2</sup>e<sup>x<sup>2</sup></sup> dx can't be asked in Extn 1 - perhaps you have the wrong question?
Any Extn 2 students who have done the integration topic, this could be turned into an interesting Extn 2 question, as follows:
Take I<sub>n</sub> = int x<sup>n</sup>e<sup>x<sup>2</sup></sup> dx, for n a non-negative integer.
Establish a reduction formula relating I<sub>n</sub> and I<sub>n-2</sub>, for integers n => 2.
From this, you can prove that you can easily find integrals of x<sup>n</sup>e<sup>x<sup>2</sup></sup> for odd n, but not for even n, as int e<sup>x<sup>2</sup></sup> dx cannot be found for elementary functions.
Any Extn 2 students who have done the integration topic, this could be turned into an interesting Extn 2 question, as follows:
Take I<sub>n</sub> = int x<sup>n</sup>e<sup>x<sup>2</sup></sup> dx, for n a non-negative integer.
Establish a reduction formula relating I<sub>n</sub> and I<sub>n-2</sub>, for integers n => 2.
From this, you can prove that you can easily find integrals of x<sup>n</sup>e<sup>x<sup>2</sup></sup> for odd n, but not for even n, as int e<sup>x<sup>2</sup></sup> dx cannot be found for elementary functions.
George W. Bush
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I(n)= 1/2 (x^n-1 e^x^2) - (n-1)/2 I (n-2) i think.
From this n must be odd as xe^x^2 can be integrated, but not e^x^2.
From this n must be odd as xe^x^2 can be integrated, but not e^x^2.