Advertisements
Advertisements
प्रश्न
`int dx/sqrt(9x - 4x^2)` equals:
पर्याय
`1/9 sin^-1 ((9x - 8)/8) + C`
`1/2 sin^-1 ((8x - 9)/9) + C`
`1/3 sin^-1 ((9x - 8)/8) + C`
`1/2 sin^-1 ((9x - 8)/9) + C`
Advertisements
उत्तर
`1/2 sin^-1 ((8x - 9)/9) + C`
Explanaton:
Let `I = int dx/sqrt(9x^2 - 4x^2)`
`= 1/2 int dx/sqrt(9/4 x - x^2)`
`= 1/2 int dx/(sqrt(- (x^2 - 9/4 x)))`
`= 1/2 dx/sqrt(- (x^2 - 9/4 + 81/64) + 81/64)`
`= 1/2 int dx/sqrt(81/64 - (x - 9/8)^2) ... [because int 1/(a^2 - x^2) dx = sin^-1 x/a]`
`= 1/2 sin^-1 ((x - 9/8)/(9/8)) +C`
`= 1/2 sin^-1 ((8x - 9)/9) + C`
APPEARS IN
संबंधित प्रश्न
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find `int (dx)/sqrt(4x - x^2)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
What is a standard integral?
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which expression is the general transformation obtained by completing the square?
What is the completed-square form of \[x^2-6x+13\]?
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
