Ex 7.2, 5 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.2, 5 (Method 1) Integrate the function: sin + cos + Step 1: Let sin + = Differentiating both sides . . . cos ( + ) . + = cos ( + ) +0 = cos ( + ) . = = . cos + Step 2: Integrating the function sin ( + ) cos ( + ) . Putting = + & dx = . cos + = . cos + . . cos + = 1 . = 1 1+1 1 +1 + 1 = 1 2 2 + 1 = 2 2 + 1 = 2 2 + = sin 2 + 2 + We know that cos 2 =1 2 sin 2 cos 2 + =1 2 sin 2 + 2 sin 2 + =1 cos 2 + sin 2 + = 1 2 1 2 cos 2 + Putting in (1) = 1 2 2 1 2 2 cos 2 + + = + + Ex 7.2, 5 (Method 2) Integrate the function: sin ( + ) cos ( + ) Step 1: Taking the given function sin + cos + = 1 2 sin 2 + = 1 2 sin 2 +2 Step 2: Let 2 +2 = Let 2 +2 = Differentiating both sides . . . 2 +0= 2 = 2 . = = 2 Step 3: Integrating the function sin ( + ) cos ( + ) . = 1 2 sin (2 +2 ) . Putting =2 +2 & = 2 = 1 2 sin ( ) . 2 = 1 4 sin ( ) . = 1 4 cos + 1 = 1 4 . cos + 1 4 = 1 4 . cos + = 1 4 . cos (2 +2 ) + = . ( + ) +
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo