Subscribe to our Youtube Channel - https://you.tube/teachoo
Ex 7.2, 5 - Chapter 7 Class 12 Integrals
Last updated at July 11, 2018 by Teachoo
Transcript
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 ) + = . ( + ) +
Ex 7.2
Ex 7.2, 1
Ex 7.2, 2
Ex 7.2, 3 Important
Ex 7.2, 4
Ex 7.2, 5 You are here
Ex 7.2, 6
Ex 7.2, 7 Important
Ex 7.2, 8
Ex 7.2, 9
Ex 7.2, 10
Ex 7.2, 11 Important
Ex 7.2, 12
Ex 7.2, 13
Ex 7.2, 14 Important
Ex 7.2, 15
Ex 7.2, 16
Ex 7.2, 17
Ex 7.2, 18
Ex 7.2, 19 Important
Ex 7.2, 20 Important
Ex 7.2, 21
Ex 7.2, 22
Ex 7.2, 23
Ex 7.2, 24
Ex 7.2, 25
Ex 7.2, 26 Important
Ex 7.2, 27
Ex 7.2, 28
Ex 7.2, 29
Ex 7.2, 30
Ex 7.2, 31
Ex 7.2, 32 Important
Ex 7.2, 33 Important
Ex 7.2, 34 Important
Ex 7.2, 35
Ex 7.2, 36 Important
Ex 7.2, 37 Important
Ex 7.2, 38 Important
Ex 7.2, 39 Important
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.