Advertisements
Advertisements
प्रश्न
Find `int (dx)/sqrt(4x - x^2)`
Advertisements
उत्तर
Let I = `int (dx)/sqrt(4x - x^2)`
= `int (dx)/sqrt(-(x^2 - 4x))`
= `int (dx)/sqrt(-(x^2 - 4x + 2^2 - 2^2))`
= `int (dx)/sqrt(-(x - 2)^2 - 2^2)`
= `int (dx)/sqrt(2^2 - (x - 2)^2)`
= `sin^-1 ((x - 2)/2) + C` ...`[∵ int (dx)/sqrt(a^2 - x^2) = sin^-1 (x/a) + C]`
APPEARS IN
संबंधित प्रश्न
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
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_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
Find: `int (dx)/(x^2 - 6x + 13)`
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which method transforms \[\int\frac{dx}{ax^2+bx+c}\] or \[\int\frac{dx}{\sqrt{ax^2+bx+c}}\] into an expression compatible with standard formulae?
What is \[\frac{d}{dx}(ax^2+bx+c)\]?
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
