Integration Full Chapter Explained - Integration Class 12 - Everything you need


Last updated at May 29, 2018 by Teachoo
Transcript
Ex 7.2, 24 2 cos𝑥 − 3 sin𝑥6 cos𝑥 + 4 sin𝑥 Step 1: Let 6 cos𝑥 + 4 sin𝑥=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 −6 sin𝑥 + 4 co𝑠𝑥= 𝑑𝑡𝑑𝑥 4 cos𝑥−6 sin𝑥𝑑𝑥 =𝑑𝑡 𝑑𝑥 = 𝑑𝑡4 cos𝑥 − 6 sin𝑥 Step 2: Integrating the function 2 cos𝑥 − 3 sin𝑥6 cos𝑥 + 4 sin𝑥 . 𝑑𝑥 Putting 6 𝑐𝑜𝑠𝑥+4 𝑠𝑖𝑛𝑥=𝑡 & 𝑑𝑥= 𝑑𝑡4 cos𝑥 − 6 sin𝑥 = 2 cos𝑥 − 3 sin𝑥𝑡 . 𝑑𝑥 = 2 cos𝑥 − 3 sin𝑥𝑡 . 𝑑𝑡4 cos𝑥 − 6 sin𝑥 = 2 cos𝑥 − 3 sin𝑥𝑡 . 𝑑𝑡2 2 cos𝑥 − 3 sin𝑥 = 12𝑡. 𝑑𝑡 = 12 𝑑𝑡𝑡 = 12 log 𝑡+𝐶1 = 12 log 4 sin𝑥+6 cos𝑥+𝐶1 = 12 log 2 2 sin𝑥+3 cos𝑥+𝐶1 = 12 log 2+𝑙𝑜𝑔 2 sin𝑥+3 cos𝑥+𝐶1 = 12 log 2+ 12 𝑙𝑜𝑔 2 sin𝑥+3 cos𝑥+𝐶1 = 𝟏𝟐 𝒍𝒐𝒈 𝟐 𝒔𝒊𝒏𝒙+𝟑 𝒄𝒐𝒔𝒙+𝑪
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