Ex 7.8, 12 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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Ex 7.8, 12 ∫_0^(πœ‹/2)β–’γ€–π‘π‘œπ‘ 2 π‘₯ 𝑑π‘₯γ€— Step 1 :- Let F(π‘₯)=∫1β–’γ€–π‘π‘œπ‘ ^2 π‘₯ 𝑑π‘₯γ€— = ∫1β–’(cos⁑2π‘₯ + 1)/2 𝑑π‘₯ =1/2 ∫1β–’γ€–π‘π‘œπ‘  2π‘₯ 𝑑π‘₯+1/2 ∫1▒𝑑π‘₯γ€— =1/2 Γ— (𝑠𝑖𝑛 2π‘₯)/2+π‘₯/2 =1/4 𝑠𝑖𝑛 2π‘₯+ π‘₯/2 Hence , F(π‘₯)=1/4 𝑠𝑖𝑛 2π‘₯+ π‘₯/2 Step 2 :- ∫_0^(πœ‹/2)β–’γ€–π‘π‘œπ‘ ^2 π‘₯=𝐹(πœ‹/2)βˆ’πΉ(0) γ€— =1/4 𝑠𝑖𝑛(2 Γ—πœ‹/2)+((πœ‹/2))/2βˆ’1/4 𝑠𝑖𝑛(2Γ—0/2)βˆ’0/2 =1/4 𝑠𝑖𝑛(πœ‹)+πœ‹/4βˆ’1/4 γ€– sin〗⁑〖0 βˆ’0γ€— =1/4 Γ—0+ πœ‹/4βˆ’ 1/4 Γ—0βˆ’0 = 𝝅/πŸ’

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