Check sibling questions

Ex 7.2, 24 - Integrate (2 cosx - 3 sinx) / (6cos x + 4sin x) - Integration by substitution - Trignometric - Normal

Ex 7.2, 24 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 24 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Ex 7.2, 24 2 cos﷮𝑥 − 3 sin﷮𝑥﷯﷯﷮6 cos﷮𝑥 + 4 sin﷮𝑥﷯﷯﷯ Step 1: Let 6 cos﷮𝑥 + 4 sin﷮𝑥﷯﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 −6 sin﷮𝑥 + 4 co𝑠﷮𝑥﷯﷯= 𝑑𝑡﷮𝑑𝑥﷯ 4 cos﷮𝑥﷯−6 sin﷮𝑥﷯﷯𝑑𝑥 =𝑑𝑡 𝑑𝑥 = 𝑑𝑡﷮4 cos﷮𝑥﷯ − 6 sin﷮𝑥﷯﷯ Step 2: Integrating the function ﷮﷮ 2 cos﷮𝑥 − 3 sin﷮𝑥﷯﷯﷮6 cos﷮𝑥 + 4 sin﷮𝑥﷯﷯﷯ ﷯. 𝑑𝑥 Putting 6 𝑐𝑜𝑠﷮𝑥+4 𝑠𝑖𝑛﷮𝑥﷯﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮4 cos﷮𝑥﷯ − 6 sin﷮𝑥﷯﷯ = ﷮﷮ 2 cos﷮𝑥 − 3 sin﷮𝑥﷯﷯﷮𝑡﷯ ﷯. 𝑑𝑥 = ﷮﷮ 2 cos﷮𝑥 − 3 sin﷮𝑥﷯﷯﷮𝑡﷯ ﷯. 𝑑𝑡﷮4 cos﷮𝑥﷯ − 6 sin﷮𝑥﷯﷯ = ﷮﷮ 2 cos﷮𝑥 − 3 sin﷮𝑥﷯﷯﷯﷮𝑡﷯ ﷯. 𝑑𝑡﷮2 2 cos﷮𝑥﷯ − 3 sin﷮𝑥﷯﷯﷯ = ﷮﷮ 1﷮2𝑡﷯﷯. 𝑑𝑡 = 1﷮2﷯ ﷮﷮ 𝑑𝑡﷮𝑡﷯﷯ = 1﷮2﷯ log﷮ 𝑡﷯﷯+𝐶1 = 1﷮2﷯ log﷮ 4 sin﷮𝑥﷯+6 cos﷮𝑥﷯﷯﷯+𝐶1 = 1﷮2﷯ log﷮ 2 2 sin﷮𝑥﷯+3 cos﷮𝑥﷯﷯﷯﷯+𝐶1 = 1﷮2﷯ log 2+𝑙𝑜𝑔 2 sin﷮𝑥﷯+3 cos﷮𝑥﷯﷯﷯+𝐶1 = 1﷮2﷯ log 2+ 1﷮2﷯ 𝑙𝑜𝑔 2 sin﷮𝑥﷯+3 cos﷮𝑥﷯﷯+𝐶1 = 𝟏﷮𝟐﷯ 𝒍𝒐𝒈 𝟐 𝒔𝒊𝒏﷮𝒙﷯+𝟑 𝒄𝒐𝒔﷮𝒙﷯﷯+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.