AP EAMCET · Maths · Definite Integration
\(\int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{1}{\sqrt[5]{x^{30}+x^{25}}} d x=\)
- A \(\frac{65}{4}\)
- B \(\frac{-75}{4}\)
- C \(\frac{75}{4}\)
- D \(\frac{-65}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{-65}{4}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{d x}{\sqrt[5]{x^{30}+x^{25}}} \Rightarrow I=\int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{d x}{x^6\left(1+x^{-5}\right)^{1 / 5}}\) \(1+x^{-5}=t \Rightarrow d t=-5 x^{-6} d x\)…
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