Ex 7.11

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Chapter 7 Class 12 Integrals

Serial order wise

Last updated at Dec. 11, 2021 by Teachoo

Ex 7.11, 1 By using the properties of definite integrals, evaluate the integrals : β«_0^(π/2)βγcos^2β‘π₯ ππ₯γ Let π=β«_π^(π /π)βγγπππγ^πβ‘π π πγ I=β«_π^(π /π)βγγππ¨π¬γ^πβ‘ (π /πβπ)π πγ I= β«_π^((π )/π)βγγπ¬π’π§γ^π πγβ‘π π Using P4 : β«_0^πβγπ(π₯)ππ₯=γ β«_0^πβπ(πβπ₯)ππ₯ (As cos (π/2βπ)=sinβ‘π) β¦(2) Adding (1) and (2) I+I= β«_0^(π/2)βγcos^2β‘π₯ ππ₯γ + β«_0^((π )/2)βγsin^2 π₯γβ‘ππ₯ 2I= β«_0^((π )/2)β(cos^2β‘γπ₯+sin^2β‘π₯ γ )β‘ππ₯ ππ =β«_π^((π )/π)βγπ .γβ‘π π 2I=[π₯]_0^(π/2) 2I =π/2β0 2I =π/2 π=π /π