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Definite Integration by properties - P4
Ex 7.11, 2
Ex 7.11, 3 Important
Example 34 Important
Ex 7.11, 4
Ex 7.11, 15
Ex 7.11, 17
Ex 7.11, 21 (MCQ) Important
Ex 7.11, 19
Ex 7.11, 12 Important
Ex 7.11, 9
Ex 7.11,7 Important
Example 32
Misc 44 (MCQ) Important
Ex 7.11, 10 Important
Ex 7.11,8 Important
Example 36 Important
Ex 7.11, 16 Important
Misc 32 Important
Example 44 Important
Definite Integration by properties - P4
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