Advertisements
Advertisements
प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Advertisements
उत्तर
Let I `= int sin x sin (cos x) dx`
Put cos x = t
= - sin x dx = dt
Hence, I `= - int sin t dt`
= (cos t) + C
= cos (cos x) + C
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int 1/(x(x-1)) 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\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^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 (e^x(x - 1))/x^2*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
`int sqrt(1 + "x"^2) "dx"` =
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int logx/x "d"x`
`int x^x (1 + logx) "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int(cos 2x)/sinx dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
