Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 7.2, 5 - Chapter 7 Class 12 Integrals
Last updated at May 29, 2023 by Teachoo
Ex 7.2
Ex 7.2, 1
Ex 7.2, 2
Ex 7.2, 3 Important
Ex 7.2, 4
Ex 7.2, 5 Important You are here
Ex 7.2, 6
Ex 7.2, 7 Important
Ex 7.2, 8
Ex 7.2, 9
Ex 7.2, 10 Important
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 Important
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 Important
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
Ex 7.2, 38 (MCQ) Important
Ex 7.2, 39 (MCQ) Important
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 ) + = . ( + ) +
