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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Definite Integration

BITSAT 2021 · Mathematics · Definite Integration

∫_ -a ^ 4 (x^ 8 -x^ 4 +x^ 2 +1) d x=2 ∫_ 0 ^ 4 (x^ 8 -x^ 4 +x^ 2...

∫−a4(x8−x4+x2+1)dx=2∫04(x8−x4+x2+1)dx\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=

Options

  1. A3
  2. B4
  3. C6
  4. D8

Correct answer

B. 4

Step-by-step solution

If f(x)\mathrm{f}(x) is an even function then ∫−aaf(x)dx=2∫0af(x)dx\int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x Here f(x)=x8−x4+x2+1\mathrm{f}(x)=x^{8}-x^{4}+x^{2}+1 is an even function, therefore a=4a=4.
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