MHT CET · Maths · Definite Integration
\(\int_{-8}^{8} \frac{x^{5}+x^{3}}{4-x^{2}} d x=\)
- A 16
- B 0
- C 8
- D \(-8\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Let \(\quad I=\int_{-8}^{8} \frac{x^{5}+x^{3}}{4-x^{2}} d x\)
Let \(f(x)=\frac{x^{5}+x^{3}}{4-x^{2}} \Rightarrow f(-x)=\frac{-\left(x^{5}+x^{3}\right)}{4-x^{2}}\)
\(\therefore \quad \mathrm{f}(-\mathrm{x})=-\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{I}=0\)
Let \(f(x)=\frac{x^{5}+x^{3}}{4-x^{2}} \Rightarrow f(-x)=\frac{-\left(x^{5}+x^{3}\right)}{4-x^{2}}\)
\(\therefore \quad \mathrm{f}(-\mathrm{x})=-\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{I}=0\)
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