# Ex 7.11, 11 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at Dec. 20, 2019 by Teachoo

Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.11, 11 By using the properties of definite integrals, evaluate the integrals : β«_((β π)/2)^(π/2)βγ sin^2γβ‘π₯ ππ₯ This is of form β«_(βπ)^πβπ(π₯)ππ₯ where π(π₯)=sin^2β‘π₯ π(βπ₯)=sin^2β‘(βπ₯)=(βπ πππ₯)^2=sin^2β‘π₯ β΄ π(π₯)=π(βπ₯) Using the Property β«_(βπ)^πβγπ(π₯)ππ₯=2,γ β«_0^πβγπ(π₯)ππ₯ γ if f(βπ₯)=π(π₯) β΄ β«_((βπ)/2)^(π/2)βγsin^2β‘γπ₯ ππ₯γ=2β«_0^(π/2)βγγπππγ^π π ππ₯γγ =2β«_0^(π/2)β[(π β πππβ‘ππ)/π]ππ₯ =β«_0^(π/2)βγ(1βcosβ‘2π₯ ) ππ₯γ = [π₯ βsinβ‘2π₯/2]_0^(π/2) = [π/2βsinβ‘2(π/2)/2]β [0βsinβ‘γ2(0)γ/2] = π/2βsinβ‘π/2β0 = π/2β0+0 = π /π β΅ cos 2x = 1 β 2 γπ ππγ^2 π₯ β 2 γπ ππγ^2 π₯ = 1 β cos 2x β γπ ππγ^2 π₯ = "1 β cos 2x" /2

Ex 7.11

Ex 7.11, 1

Ex 7.11, 2

Ex 7.11, 3 Important

Ex 7.11, 4

Ex 7.11, 5 Important

Ex 7.11, 6

Ex 7.11,7 Important

Ex 7.11,8 Important

Ex 7.11, 9

Ex 7.11, 10 Important

Ex 7.11, 11 Important You are here

Ex 7.11, 12 Important

Ex 7.11, 13

Ex 7.11, 14

Ex 7.11, 15

Ex 7.11, 16 Important

Ex 7.11, 17

Ex 7.11, 18 Important

Ex 7.11, 19

Ex 7.11, 20 (MCQ) Important

Ex 7.11, 21 (MCQ) Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.