Ex 7.10, 11 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Ex 7.10
Ex 7.10, 1
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Ex 7.10, 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₯) 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
