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∫-55 x7x4+10 dx = ______. - Mathematics and Statistics

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Question

$\int_{- 5}^{5} \frac{x^{7}}{x^{4} + 10} d x$ = ______.

Options

10
5
0
$\frac{1}{5}$

MCQ

Fill in the Blanks

Solution

$\int_{- 5}^{5} \frac{x^{7}}{x^{4} + 10} d x$ = 0.

Explanation:

Let f(x) = $\frac{x^{7}}{x^{4} + 10}$

∴ f(– x) = $\frac{{(- x)}^{7}}{{(- x)}^{4} + 10} = \frac{- x^{7}}{x^{4} + 10}$

= – f(x)

∵ f(– x) = – f(x)

∴ f(x) is an odd function

∴ $\int_{- a}^{a} f (x) . d x$ = 0

⇒ $\int_{- 5}^{5} \frac{x^{7}}{x^{4} + 10} d x$ = 0

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Properties of Definite Integrals

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