Question
Download Solution PDFযদি \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\) হয় তবে b এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFধারণা:
\(\rm \int \frac{dx}{\sqrt {a^{2}-x^{2}}}=sin^{-1}\frac{x}{a}+C\)
গণনা:
প্রদত্ত: \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)
সূত্র ব্যবহার করে,
\(\rm \int \frac{dx}{\sqrt {a^{2}-x^{2}}}=sin^{-1}\frac{x}{a}+C\)
\(\rm \Rightarrow \int \frac{dx}{\sqrt {9-x^{2}}}=\int \frac{dx}{\sqrt {3^{2}-x^{2}}}=sin^{-1}\frac{x}{3}+C\) -----(1)
∵ প্রদত্ত যে, \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)- ----(2)
(1) ও (2) তুলনা করে আমরা পাই b = 3
সুতরাং, সঠিক উত্তর বিকল্প 2
Last updated on Jun 18, 2025
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