Definite Integration by Reduction Methods

Февраль 11, 2021

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Definite Integration by Reduction Methods

Содержание

2. Consider
3. Consider
4. Using exactly the same method obtains exactly the same result. Hence, Now consider
5. Using this reduction formula successively Repeatedly applying the formula, we find that:
6. Using this reduction formula successively The final term will depend on if n is even or
7. Using this reduction formula successively If n is odd: Also: Hence in both cases, when n
8. Example Evaluate n is even so, Hence,
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Слайд 2

Consider

Consider

Слайд 3

Consider

Consider

Слайд 4

Using exactly the same method obtains exactly the same result.
Hence,
Now consider

Using exactly the same method obtains exactly the same result. Hence, Now consider

Слайд 5

Using this reduction formula successively
Repeatedly applying the formula, we find that:

Using this reduction formula successively Repeatedly applying the formula, we find that:

Слайд 6

Using this reduction formula successively
The final term will depend on if n

Using this reduction formula successively The final term will depend on if

is even or odd.
If n is even:
Also:
Hence in both cases, when n is even:

Слайд 7

Using this reduction formula successively
If n is odd:
Also:
Hence in both cases, when

Using this reduction formula successively If n is odd: Also: Hence in

n is odd:

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Example
Evaluate
n is even so,
Hence,

Example Evaluate n is even so, Hence,