
Ex 7.8
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.8, 4 β«_0^(π/4)βsinβ‘2π₯ππ₯ Let F(π₯)=β«1βγπ ππ 2π₯ ππ₯γ =1/2 (βπππ 2π₯) =(β1)/( 2) πππ 2π₯ Hence, F(π₯)=(β1)/( 2) πππ 2π₯ Now, β«_0^(π/4)βγπ ππ2π₯ ππ₯γ=πΉ(π/4)βπΉ(0) =(β1)/( 2) πππ (2 Γ π/4)β((β1)/( 2) πππ (2 Γ0)) =(β1)/( 2) πππ π/2+1/2 πππ 0 =(β1)/( 2) Γ0+1/2 Γ1 = π/π