The value of _{-1}¹ \;{x³}{x²+2≤ft|x|+1} dx ... - CBSE Class 12 ...

CBSE Class 12 Math 2026 All Sets Solved Paper

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Question : 9 of 20

Marks: +1, -0

The value of

\int\limits_{-1}^{1} \;\frac{x^{3}}{x^{2}+2\left|x\right|+1} dx

is

0
$\log 2$
$2\log 2$
$\;\frac{1}{2} \log 2$

Solution:

I=\int\limits_{-1}^{1} \;\frac{x^{3}}{x^{2}+2\left|x\right|+1} dx

.....(i)

Then, by using the property

\int\limits_{a}^{b} f(x) dx=\int\limits_{a}^{b} f(a+b-x) dx

I=\int\limits_{-1}^{1} \;\frac{-x^{3}}{x^{2}+2\left|x\right|+1} dx

.......(ii)

adding (i) & (ii)

2I = 0

\Rightarrow I=0

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