Ex 7.11, 11
Last updated at Dec. 8, 2016 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₯ π(π₯)=sin^2β‘π₯ π(βπ₯)=sin^2β‘(βπ₯)=(βπ πππ₯)^2=sin^2β‘π₯ β΄ π(π₯)=π(βπ₯) β΄ β«_((βπ)/2)^(π/2)βγsin^2β‘γπ₯ ππ₯γ=2β«_0^(π/2)βγsin^2 π₯ ππ₯γγ =2β«_0^(π/2)β[(1 β cosβ‘2π₯)/2]ππ₯ =β«_0^(π/2)βγ(1βcosβ‘2π₯ ) ππ₯γ = [π₯ βsinβ‘2π₯/2]_0^(π/2) = π/2βsinβ‘2(π/2)/2β0+sinβ‘γ2(0)γ/2 = π/2βsinβ‘π/2+sinβ‘0/2 = π/2β0+0 = π/2
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