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प्रश्न
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
विकल्प
10
5
0
`1/5`
उत्तर
`int_(-5)^5 x^7/(x^4 + 10) dx` = 0.
Explanation:
Let f(x) = `x^7/(x^4 + 10)`
∴ f(– x) = `(-x)^7/((-x)^4 + 10) = (-x^7)/(x^4 + 10)`
= – f(x)
∵ f(– x) = – f(x)
∴ f(x) is an odd function
∴ `int_(-a)^a f(x).dx` = 0
⇒ `int_(-5)^5 x^7/(x^4 + 10) dx` = 0
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