Evaluate

∫ (x 3 + 1) dx from -2 to 2

Slide42.JPG

Slide43.JPG
Slide44.JPG

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 17 โˆซ (x3 + 1) dx from -2 to 2 This is of form โˆซ a -a f (x) dx And we now that โˆซ_(โˆ’๐‘Ž)๐‘Ž ๐‘“(๐‘ฅ)๐‘‘๐‘ฅ=0,ใ€— if f(โˆ’๐‘ฅ)=โˆ’๐‘“(๐‘ฅ) And โˆซ_(โˆ’๐‘Ž)^๐‘Ž๐‘“(๐‘ฅ)๐‘‘๐‘ฅ=2โˆซ_0^๐‘Ž๐‘“(๐‘ฅ)๐‘‘๐‘ฅ , if f(โˆ’๐‘ฅ)=๐‘“(๐‘ฅ) Now, โˆซ_(โˆ’2)^2(๐‘ฅ^3+1)๐‘‘๐‘ฅ = โˆซ_(โˆ’2)^2 ๐‘ฅ^3 ๐‘‘๐‘ฅใ€— + โˆซ_(โˆ’2)^21๐‘‘๐‘ฅ Since ใ€–(โˆ’๐‘ฅ)ใ€—^3=โˆ’๐‘ฅ^3 So, โˆซ_(โˆ’๐‘Ž)^๐‘Žโ–’ใ€–๐‘ฅ^3 ๐‘‘๐‘ฅ=0,ใ€— And 1 is constant, so f(โ€“x) = f(x) โˆซ_(โˆ’๐‘Ž)^๐‘Žโ–’1๐‘‘๐‘ฅ=2โˆซ_0^๐‘Žโ–’๐‘‘๐‘ฅ = 0 + 2โˆซ_0^2โ–’1๐‘‘๐‘ฅ = 2โˆซ_0^2โ–’๐‘‘๐‘ฅ = 2 ใ€–[๐‘ฅ]ใ€—_0^2 = 2 (2 โ€“ 0) = 4

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.