Advertisements
Advertisements
प्रश्न
Integrate the function:
`sqrt(4 - x^2)`
Advertisements
उत्तर
Let `I = int sqrt (4 - x^2) dx`
`= int sqrt ((2)^2 - x^2) dx`
`= [x /2 sqrt ((2)^2 - x^2) + 4/2 sin^-1 (x/2)] + C` `...[int sqrt (a^2 - x^2) dx = x/2 sqrt (a^2 - x^2) + a^2/2 sin^-1 (x/a) + C]`
`= (x sqrt 4 - x^2)/2 + 4/2 sin^-1 (x/2) +C`
`(x sqrt(4 - x^2))/2 + 2 sin^-1 (x/2) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
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 `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
`int dx/(x^2 + 2x + 2)` equals:
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(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
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`
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
