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प्रश्न
Using second fundamental theorem, evaluate the following:
`int_0^1 x"e"^(x^2) "d"x`
योग
उत्तर
`int_0^1 x"e"^(x^2) "d"x = 1/2 int_0^1 2x"e"^(x^2) "d"x`
Let t = x2
Then dt = 2x dx
When x = 0, t = 0
x = 1, t = 1
So the integral becomes,
`1/2int_0^2 "e"^"t" "dt" = 1/2 ["e"^"t"]_0^1`
= `1/2 ["e" - 1]`
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Definite Integrals
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