
Introducing your new favourite teacher - Teachoo Black, at only βΉ83 per month
Definite Integration by properties - P7
Definite Integration by properties - P7
Last updated at Aug. 9, 2021 by Teachoo
Ex 7.11, 20 The value of β«_((β π)/2)^(π/2)βγ(π₯^3+π₯ πππ π₯+tan^5β‘γπ₯+1γ ) ππ₯γ (A) 0 (B) 2 (C) π (D) 1 β«_((βπ)/2)^(π/2)βγ (π₯^3+π₯ πππ π₯+tan^5β‘γπ₯+1γ ) ππ₯γ We know that β«_(βπ)^(+π)βγπ(π₯) ππ₯γ={β(0, ππ π(βπ₯)=βπ(π₯)@&2β«_0^πβγπ(π₯) ππ₯γ, ππ π(βπ₯)=π(π₯) )β€ Thus, our equation becomes β«_((β π)/2)^(π/2)βγ(π₯^3+π₯ πππ π₯+tan^5β‘γπ₯+1γ ) ππ₯γ = β«_0^(π/2)βγ0 ππ₯+β«_0^(π/2)βγ0 ππ₯+β«_0^(π/2)βγ0 ππ₯+πβ«_π^(π /π)βπ πγγγ = 2β«_0^(π/2)βππ₯ = 2 [π₯]_0^(π/2) = 2(π/2β0) =π Thus, correct option is C