Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Advertisements
उत्तर
`int (1)/sqrt(11 - 4x^2).dx`
= `int (1)/sqrt((sqrt(11))^2 - (2x)^2).dx`
= `(1)/(2) sin^-1 (2x/sqrt(11)) + c`.
APPEARS IN
संबंधित प्रश्न
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
`int logx/(log ex)^2*dx` = ______.
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int 1/(xsin^2(logx)) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int sqrt(x^2 - a^2)/x dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate `int 1/(x(x-1))dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
