Ex 7.2, 15 Integrate the function: 𝑥﷮9 − 4𝑥2﷯ Step 1: Let 9 – 4𝑥2 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0−4.2 𝑥﷮2−1﷯= 𝑑𝑡﷮𝑑𝑥﷯ −8𝑥.𝑑𝑥=𝑑𝑡 𝑑𝑥 = 𝑑𝑡﷮−8𝑥﷯ Step 2: Integrating the function ﷮﷮ 𝑥﷮9 − 4𝑥2﷯﷯ . 𝑑𝑥 Putting 9 − 4𝑥2=𝑡 & 𝑑𝑥= 𝑑𝑡﷮−8𝑥﷯ = ﷮﷮ 𝑥﷮𝑡﷯﷯ . 𝑑𝑡﷮−8𝑥﷯ = − 1﷮8﷯ ﷮﷮ 1﷮𝑡﷯﷯ . 𝑑𝑡 = − 1﷮8﷯ log ﷮ 𝑡﷯﷯+𝐶 = − 𝟏﷮𝟖﷯ 𝐥𝐨𝐠 ﷮ 𝟗 − 𝟒𝒙𝟐﷯﷯+𝑪

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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