Advertisements
Advertisements
प्रश्न
उत्तर
\[\int \sqrt{9 - x^2} \text{ dx}\]
\[ = \int \sqrt{3^2 - x^2} \text{ dx}\]
\[ = \frac{x}{2}\sqrt{3^2 - x^2} + \frac{3^2}{2} \sin^{- 1} \left( \frac{x}{3} \right) + C \left[ \because \int\sqrt{a^2 - x^2} \text{ dx } = \frac{1}{2}x\sqrt{a^2 - x^2} + \frac{1}{2} a^2 \text{ sin}^{- 1} \left( \frac{x}{a} \right) + C \right]\]
\[ = \frac{x}{2}\sqrt{9 - x^2} + \frac{9}{2} \sin^{- 1} \left( \frac{x}{3} \right) + C\]
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals : `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
`int sqrt(1 + "x"^2) "dx"` =
Evaluate: `int "e"^sqrt"x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
