NCERT Exemplar MCQ

Chapter 7 Class 12 Integrals
Serial order wise

## (D) aβ« 0^a f(x) dx

This question is similar to Ex 7.11, 19 - Chapter 7 Class 12 - Integrals

Get live Maths 1-on-1 Classs - Class 6 to 12

### Transcript

Question 5 If π "and" π are continuous functions in [0, 1] satisfying π(π₯)=π(πβπ₯) and π(π₯)+π (πβπ₯)=π, then β«1_0^πβγπ(π₯). π(π₯)γ ππ₯ is equal to π/2 (B) π/2 β«1_0^πβγπ(π₯) ππ₯γ (C) β«1_0^πβγπ(π₯) ππ₯γ (D) πβ«1_0^πβγπ(π₯) ππ₯γ Let π° =β«_π^πβπ(π) π(π) ππ Using g(π₯)+π(πβπ₯)=π I =β«_0^πβπ(π₯) [πβπ(πβπ₯)] ππ₯ I = β«_0^πβ[π.π(π₯)βπ(π₯)π(πβπ₯)] ππ₯ π° =πβ«_π^πβγπ(π)ππββ«_π^πβγπ(π) π(πβπ) γγ ππ I =πβ«_0^πβγπ(π₯)ππ₯ββ«_π^πβγπ(πβπ) π(πβ(πβπ)) γγ ππ₯ I =πβ«_0^πβγπ(π₯)ππ₯ββ«_0^πβγπ(πβπ) π(π₯) γγ ππ₯ Using π(π₯)=π(πβπ₯) I =πβ«_0^πβγπ(π₯)ππ₯ββ«_0^πβγπ(π) π(π₯) γγ ππ₯ I =πβ«_0^πβγπ(π₯)ππ₯βπγ I +I=aβ«_0^πβπ(π₯)ππ₯ 2I=aβ«_0^πβπ(π₯)ππ₯ π=π/π β«_π^πβπ(π)ππ β΄ β«_0^πβγπ(π₯) π(π₯) γ ππ₯=2β«_0^πβπ(π₯)ππ₯ Hence Proved So, the correct answer is (b)