
Ex 7.11
Ex 7.11, 2
Ex 7.11, 3 Important
Ex 7.11, 4
Ex 7.11, 5 Important
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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
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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
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