Sometimes while integrating, We get questions like ∫1▒√(𝑎^2−𝑥^2 ) 𝑑𝑥 Now, how do we solve it? There are some standard substitutions, where we put value of x and solve it √(𝑎^2−𝑥^2 ) 𝑥=𝑎 𝑠𝑖𝑛⁡𝜃 1−〖𝑠𝑖𝑛〗^2⁡𝜃=〖𝑐𝑜𝑠〗^2⁡𝜃 √(𝑎^2+𝑥^2 ) 𝑥=𝑎 𝑡𝑎𝑛⁡𝜃 1+〖𝑡𝑎𝑛〗^2⁡𝜃=〖𝑠𝑒𝑐〗^2⁡𝜃 √(𝑥^2−𝑎^2 ) 𝑥=𝑎 𝑠𝑒𝑐⁡𝜃 〖𝑠𝑒𝑐〗^2⁡𝜃−1=〖𝑡𝑎𝑛〗^2⁡𝜃

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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