The value of integral -44x20211-x2022dx- is

Let nbsp;I=∫_ 4^4x^20211+x^2022dx We know that, ∫_ a^a f(x) dx=2∫_0^a f(x) dx, if nbsp; f(x) is even 0, if nbsp; f(x) is odd ⇒ I=0 (∵ nbsp;x^20211+x^202 ...

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Standard XII

Mathematics

Higher Order Derivatives

The value of ...

Question

The value of integral $4 \int - 4 \frac{x^{2021}}{1 + x^{2022}} d x,$ is

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Solution

The correct option is A $0$
Let $I = 4 \int - 4 \frac{x^{2021}}{1 + x^{2022}} d x$
We know that,
$a \int - a f (x) d x = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 a \int 0 f (x) d x, if f (x) is even 0, if f (x) is odd \end{matrix}$
$\Rightarrow I = 0$
$(∵ \frac{x^{2021}}{1 + x^{2022}} is an odd function.)$

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The value of integral 4∫−4x20211+x2022dx, is

The correct option is A 0Let I=4∫−4x20211+x2022dx We know that, a∫−af(x) dx=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩2a∫0f(x) dx, if f(x) is even0, if f(x) is odd ⇒I=0 (∵x20211+x2022 is an odd function.)

The value of integral $4 \int - 4 \frac{x^{2021}}{1 + x^{2022}} d x,$ is