Advertisements
Advertisements
प्रश्न
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Advertisements
उत्तर
\[\int \sqrt{9 + x^2} \text{ dx }\]
\[ = \int \sqrt{3^2 + x^2} dx \left( \because \sqrt{a^2 + x^2} = \frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\text{ ln }\left| x + \sqrt{x^2 + a^2} \right| \right)\]
\[ = \frac{x}{2}\sqrt{9 + x^2} + \frac{9}{2}\text{ ln }\left| x + \sqrt{9 + x^2} \right| + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate `int 1/((2"x" + 3))` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int(log(logx) + 1/(logx)^2)dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int 1/(x^2+4x-5) dx`
`int x^3 e^(x^2) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x-1))dx`
