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प्रश्न
Integrate the following with respect to x.
xe–x
सारिणी
योग
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उत्तर
= `int x"e"^-x "d"x`
= `int "udv"`
`int "udv"` = uv – u1v1 + u11v2 ........
`int x"e"^-x "d"x = (x)(- "e"^-x) - (1)"e"^-x + "c"`
= – xe–x – e–x + c
= – e-x(x + 1) + c
| Successive derivatives | Repeated Integrals |
|
Take u = x uI = 1 uII = 0 |
and dv = e–x dx `int "dv" = int "e"^-x "d"x` v = `"e"^-x/(-1)` v = `- "e"^-x` v1 = `int -"e"^-x "d"x` = `- ["e"^-x/-1]` v1 = e–x |
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