Advertisements
Advertisements
प्रश्न
If `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`, then the value of k is:
विकल्प
3
2
1
None of the above options
उत्तर
3
Explanation:
Given, `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`
Taking L.H.S. = `int (log "x")^2/"x" "dx"`
Let, log x = t
∴ `1/"x" "dx" = "dt"`
= `int "t"^2"dt" = "t"^3/3 + "c"`
Substituting the value of t,
= `(log "x")^3/3 + "c"`
On comparing with R.H.S. we get
k = 3
APPEARS IN
संबंधित प्रश्न
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Evaluate : `int _0^(pi/2) "sin"^ 2 "x" "dx"`
Prove that `int _a^b f(x) dx = int_a^b f (a + b -x ) dx` and hence evaluate `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tan x))` .
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
Evaluate `int_1^3 x^2*log x "d"x`
`int (cos x + x sin x)/(x(x + cos x))`dx = ?
`int_0^{pi/2} log(tanx)dx` = ______
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int_(-pi/4)^(pi/4) log|sinx + cosx|"d"x`
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - x)dx`
The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.
The value of `int_0^(π/4) (sin 2x)dx` is ______.
Evaluate: `int_-1^1 x^17.cos^4x dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
