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
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int sqrt(1 + sin2x) dx`
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
