Check sibling questions

Ex 7.11,7 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at Dec. 20, 2019 by

Ex 7.11, 7 - Evaluate using properties x (1 - x)n dx - Ex 7.11

Ex 7.11,7 - Chapter 7 Class 12 Integrals - Part 2

Solve all your doubts with Teachoo Black (new monthly pack available now!)

Join Teachoo Black

Transcript

Ex 7.11,7 By using the properties of definite integrals, evaluate the integrals : ∫_0^1β–’γ€– π‘₯(1βˆ’π‘₯)^𝑛 γ€— 𝑑π‘₯ Let I=∫_0^1β–’γ€–π‘₯(1βˆ’π‘₯)^𝑛 𝑑π‘₯γ€— ∴ I=∫_0^1β–’γ€–(1βˆ’π‘₯) [1βˆ’(1βˆ’π‘₯)]^𝑛 𝑑π‘₯γ€— I=∫_0^1β–’γ€–(1βˆ’π‘₯) [1βˆ’1+π‘₯]^𝑛 𝑑π‘₯γ€— I=∫_0^1β–’γ€–(1βˆ’π‘₯) [π‘₯]^𝑛 𝑑π‘₯γ€— I= ∫_0^1β–’γ€–(1βˆ’π‘₯) γ€– π‘₯γ€—^𝑛 𝑑π‘₯γ€— Using P4 : ∫_0^π‘Žβ–’γ€–π‘“(π‘₯)𝑑π‘₯=γ€— ∫_0^π‘Žβ–’π‘“(π‘Žβˆ’π‘₯)𝑑π‘₯ I= ∫_0^1β–’γ€–(γ€– π‘₯γ€—^π‘›βˆ’ π‘₯^(𝑛 + 1) ) 𝑑π‘₯γ€— I= ∫_0^1β–’γ€–γ€– π‘₯γ€—^𝑛 𝑑π‘₯γ€—βˆ’βˆ«_0^1β–’γ€–γ€– π‘₯γ€—^(𝑛 + 1) 𝑑π‘₯γ€— I=[π‘₯^(𝑛 + 1)/(𝑛 + 1)]_0^1βˆ’[π‘₯^(𝑛 + 2)/(𝑛 + 2)]_0^1 I=[(1)^(𝑛 + 1)/(𝑛 + 1)βˆ’(0)^(𝑛 + 1)/(𝑛 + 1)]βˆ’[(1)^(𝑛 + 2)/(𝑛 + 2)βˆ’(0)^(𝑛 + 2)/(𝑛 + 2)] I= 1/(𝑛 + 1)βˆ’1/(𝑛 + 2) I=(𝑛 + 2 βˆ’ (𝑛 + 1))/(𝑛 + 1)(𝑛 + 2) 𝐈=𝟏/(𝒏 + 𝟏)(𝒏 + 𝟐)

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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.