Advertisements
Advertisements
Question
Integrate the function `1/sqrt(8+3x - x^2)`
Advertisements
Solution
Let `I = int 1/sqrt(8 + 3x - x^2) dx`
`= int dx/sqrt(8 - (x^2 - 3x))`
`= int dx/sqrt(8 - (x^2 - 2 * 3/2 x + 9/4) + 9/4)`
`= int dx/sqrt(41/4 - (x - 3/2)^2)`
`= int dx/sqrt((sqrt41/2)^2 - (x - 3/2)^2)` `...[∵ int dx/sqrt (a^2 - x^2) = sin^-1 x/a + C]`
`= sin^-1 ((x - 3/2)/(sqrt41/2)) + C`
`= sin^-1 ((2x - 3)/sqrt41) + C`
APPEARS IN
RELATED QUESTIONS
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find `int (dx)/sqrt(4x - x^2)`
