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प्रश्न
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
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उत्तर
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an Odd function.
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संबंधित प्रश्न
By using the properties of the definite integral, evaluate the integral:
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By using the properties of the definite integral, evaluate the integral:
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(A) 1
(B) –2
(C) 2
(D) –1
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By completing the following activity, Evaluate `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x)) "d"x`.
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Using the property, `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x) "d"x`, we get
I = `int_2^5 ("( )")/(sqrt(7 - x) + "( )") "d"x` ......(ii)
Adding equations (i) and (ii), we get
2I = `int_2^5 (sqrt(x))/(sqrt(x) - sqrt(7 - x)) "d"x + ( ) "d"x`
2I = `int_2^5 (("( )" + "( )")/("( )" + "( )")) "d"x`
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Evaluate the following integral:
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Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
