Integration by parts

Chapter 7 Class 12 Integrals
Concept wise

### Transcript

Ex 7.6, 21 - Chapter 7 Class 12 Integrals - NCERT Solution Integrate e^2x sin x I = ∫ e^2x sin x dx Using ILATE e^2x -> Exponential sin x -> Trigonometric We know that ∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫ (f'(x) ∫ g(x)dx)dx Putting f(x) = e^2x, g(x) = sin x I = sin . 2 I = sin 2 sin 2 I = sin . 2 2 cos . 2 2 I = 1 2 . 2 sin 1 2 cos . 2 Solving I2 = 1 2 cos . 2 I1 = 1 2 cos . 2 = 1 2 cos 2 cos 2 = 1 2 cos . 2 2 ( sin ) . 2 2 = 1 2 2 . cos 2 + 1 2 2 sin = 1 2 2 . cos 2 + 1 2 I + 1 Putting the value of I1 in (1) , we get I = 2 sin I = 2 sin 2 1 2 2 . cos 2 + I 2 + 1 I = 2 2 sin 2 4 cos I 4 1 + I 4 = 2 sin 2 2 . cos 4 5 4 = 2 4 2 sin cos 1 = 4 5 . 2 4 2 sin cos 4 1 5 = +

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.