Ex 7.10

Chapter 7 Class 12 Integrals
Serial order wise

### Transcript

Ex 7.10, 15 By using the properties of definite integrals, evaluate the integrals : β«_0^(π/2)β(sinβ‘π₯ β cosβ‘π₯)/(1 + sinβ‘π₯ cosβ‘π₯ ) ππ₯ Let I=β«_0^(π/2)βγsinβ‘γπ₯ β cosβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯γ β΄ I=β«_0^(π/2)βγ(π ππ(π/2 β π₯) β πππ (π/2 β π₯))/(1 + π ππ(π/2 β π₯) πππ (π/2 β π₯) ) ππ₯γ I=β«_0^(π/2)βγ(cosβ‘π₯ β sinβ‘π₯)/( 1 +γ cosγβ‘π₯ sinβ‘γπ₯ γ ) ππ₯γ Adding (1) and (2)i.e. (1) + (2) I+I=β«_0^(π/2)βγ sinβ‘γπ₯ β cosβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯+γ β«_0^(π/2)βγcosβ‘γπ₯ β sinβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯γ 2I=β«_0^(π/2)βγ sinβ‘γπ₯ β cosβ‘γπ₯ +γ cosγβ‘γπ₯ β sinβ‘π₯ γ γ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) γ ππ₯ 2I=β«_0^(π/2)βγ 0/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) γ ππ₯ 2I=0 β΄ π=π