Advertisements
Advertisements
प्रश्न
`int sinx/(3 + 4cos^2x) "d"x` = ______.
Advertisements
उत्तर
`int sinx/(3 + 4cos^2x) "d"x` = `- 1/(2sqrt(3)) tan^-1 (2/sqrt(3) cos x) + "C"`.
Explanation:
Let I = `int sinx/(3 + 4cos^2x) "d"x`
Put cos x = t
∴ – sin x dx = dt
⇒ sinx dx = – dt
∴ I = `- int "dt"/(3 + 4"t"^2)`
= `- 1/4 int "dt"/(3/4 + "t"^2)`
= `- 1/4 int "dt"/((sqrt(3)/2)^2 + "t"^2)`
= `1/4 xx 1/(sqrt(3)/2) tan^-1 ("t"/(sqrt(3)/2)) + "C"`
= ` 1/(2sqrt(3)) tan^-1 ((2"t")/sqrt(3)) + "C"`
= `- 1/(2sqrt(3)) tan^-1 ((2cosx)/sqrt(3)) + "C"`
Hence I = `- 1/(2sqrt(3)) tan^-1 (2/sqrt(3) cos x) + "C"`.
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
sin4 x
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find `int dx/(x^2 + 4x + 8)`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
