Advertisements
Advertisements
Question
`int 1/sqrt(8 + 2x - x^2) dx` is equal to ______.
Options
`1/3 sin^-1((x - 1)/3) + c`
`sin^-1((x + 1)/3) + c`
`1/3 sin^-1((x + 1)/3) + c`
`sin^-1((x - 1)/3) + c`
MCQ
Fill in the Blanks
Advertisements
Solution
`int 1/sqrt(8 + 2x - x^2) dx` is equal to `underlinebb(sin^-1((x - 1)/3) + c)`.
Explanation:
`int (dx)/sqrt(8 + 2x - x^2)`
= `int (dx)/sqrt(8 + 1 - (x^2 - 2x + 1))`
= `int (dx)/sqrt(3^2 - (x - 1)^2`
= `sin^-1((x - 1)/3) + c`
shaalaa.com
Some Special Integrals
Is there an error in this question or solution?
