Chapter 7 Class 12 Integrals
Concept wise

Ex 7.8, 17 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

Slide42.JPG

Slide43.JPG

Transcript

Ex 7.8, 17 ∫_0^(πœ‹/4)β–’(2 sec^2⁑π‘₯+π‘₯^3+2) 𝑑π‘₯ Let F(π‘₯)=∫1β–’γ€–(2 sec^2⁑〖π‘₯+π‘₯^3+2γ€— ) 𝑑π‘₯γ€— =2∫1β–’γ€–sec^2⁑〖π‘₯ 𝑑π‘₯γ€—+∫1β–’γ€–π‘₯^3 𝑑π‘₯+∫1β–’γ€–2 𝑑π‘₯γ€—γ€—γ€— =2 tan⁑〖π‘₯+π‘₯^4/4+2π‘₯γ€— Hence F(π‘₯)=2 tan⁑〖π‘₯+π‘₯^4/4+2π‘₯γ€— Now, ∫_0^(πœ‹/4)β–’γ€–(2𝑠𝑒𝑐^2 π‘₯+π‘₯^3+2)𝑑π‘₯=𝐹(πœ‹/4)βˆ’πΉ(0) γ€— =[2π‘‘π‘Žπ‘› πœ‹/4+(πœ‹/4)^4/4+2 πœ‹/4]βˆ’[2π‘‘π‘Žπ‘›(0)+(0)^4/4+2 Γ—0] =2π‘‘π‘Žπ‘› πœ‹/4+πœ‹^4/4^4 Γ— 1/4+πœ‹/2βˆ’[2Γ—0+0+0] =2 Γ—1+πœ‹^4/4^5 +πœ‹/2βˆ’0 =𝟐+𝝅^πŸ’/πŸπŸŽπŸπŸ’+𝝅/𝟐

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.