Advertisements
Advertisements
प्रश्न
Find the integrals of the function:
cos 2x cos 4x cos 6x
Advertisements
उत्तर
Let `I = int cos 2x cos 4x cos 6x` dx
`= 1/2 int (2 cos 2x cos 4x) cos 6x dx`
... [∵ 2 cos A cos B = cos (A + B) - cos (A - B)]
`= 1/2 int (cos 6x + cos 2x) cos 6x dx`
`= 1/4 int 2 cos^2 6x dx + 1/4 int (2 cos 2c cos 6x) dx`
`= 1/4 int (1 + cos 12 x) dx + 1/4 int (cos 8x + cos 4x)` dx
`= 1/4 x + 1/4 ((sin 12x)/12) + 1/4 ((sin 8x)/8 + (sin 4x)/4) + C`
`= 1/4 [x + 1/12 sin 12 x + 1/8 sin 8x + 1/4 sin 4x] + C`
APPEARS IN
संबंधित प्रश्न
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
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:
`(1-cosx)/(1 + cos 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:
tan3 2x sec 2x
Find the integrals of the function:
tan4x
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int dx/(x^2 + 4x + 8)`
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
What does integration using trigonometric identities mean?
Which identity is used for \(\sin^3 x\)?
What is \(\int \cos^2 x\,dx\)?
What is \(\int \sin 2x\cos 3x\,dx\)?
After a trigonometric expression has been simplified, how should it be integrated?
What must always be added to an indefinite integral?
