Advertisements
Advertisements
प्रश्न
Integrate the function `1/sqrt(8+3x - x^2)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find:
`int(x^3-1)/(x^3+x)dx`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
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)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
Evaluate : `int_2^3 3^x dx`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
