∫_-a^4 (x^8-x^4+x^2+1 ) d x=2 ∫_0^4 (x^8-x^4+x^2+1 ) d x then a=

Correct answer: (B) 4. If f(x) is an even function then ∫_-a^a f(x) d x=2 ∫_0^a f(x) d x Here f(x)=x^8-x^4+x^2+1 is an even function, therefore a=4 .

Q61 / 125 · BITSAT 2021 · Mathematics

$\int_{-a}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x=2 \int_{0}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x$ then $a=$

A
3
Correct answer
B
4
C
6
D
8

Solution

If $\mathrm{f}(x)$ is an even function then $\int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x$ Here $\mathrm{f}(x)=x^{8}-x^{4}+x^{2}+1$ is an even function, therefore $a=4$.

Hence, the correct answer is option: 'B'.

$\int_{-a}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x=2 \int_{0}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x$ then $a=$

Solution

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