Evaluate ∫ cot 2 x d x

Given, ∫ cot 2 x d x = ∫ cosec 2 x - 1 d x = ∫ - 1 d x + ∫ cosec 2 x d x = - x + cot x + C ∴ ∫ cot 2 x d x = - x + cot x + C

Evaluate ∫ 1 + sin 2 x d x

Given, ∫ 1 + sin 2 x d x We can write it as = ∫ sin 2 x + cos 2 x + 2 sin x cos x d x ∵ sin 2 x = 2 sin x cos x & sin 2 x + cos 2 x = 1 = ∫ sin x + cos x 2 d x = ∫ ( sin x + cos x ) d x By integrating w.r.t x , ∴ ∫ 1 + sin 2 x d x = - cos x + sin x + c .

Evaluate ∫ 0 π 2 cos 2 x d x

Consider ∫ 0 π 2 cos 2 x d x . . . . . 1 I = ∫ 0 π 2 cos 2 π 2 − x d x ∵ ∫ 0 a f ( x ) d x = ∫ 0 a f ( a − x ) d x I = ∫ 0 π 2 sin 2 x d x . . . . . ( 2 ) Adding 1 and 2 , we get, 2 I = ∫ 0 π 2 cos 2 x + sin 2 x d x 2 I = ∫ 0 π 2 1 · d x 2 I = π 2 − 0 I = π 4

Evaluate ∫ 0 π 4 log 1 + tan x

Let I = ∫ 0 π 4 log 1 + tan x d x ⇒ I = ∫ 0 π 4 log 1 + tan π 4 - x d x ⇒ I = ∫ 0 π 4 log 1 + 1 - tan x 1 + tan x d x ⇒ I = ∫ 0 π 4 log 2 1 + tan x d x ⇒ I = ∫ 0 π 4 log 2 - log 1 + tan x d x ⇒ I = ∫ 0 π 4 log 2 d x - ∫ 0 π 4 log 1 + tan x d x ⇒ I = log 2 ∫ 0 π 4 d x - I ⇒ 2 I = log 2 x 0 π 4 ⇒ 2 I = π 4 log 2 ⇒ I = π 8 log 2

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Integrals>Bihar Board-2019

Embibe Experts Solutions for Chapter: Integrals, Exercise 1: Bihar Board-2020

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Integrals, Exercise 1: Bihar Board-2020

Attempt the practice questions on Chapter 7: Integrals, Exercise 1: Bihar Board-2020 with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS solutions are prepared by Experienced Embibe Experts.