मराठी

Evaluate the following: d∫dx1+cosx

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`int ("d"x)/(1 + cos x)`

बेरीज
Advertisements

उत्तर

I = `int ("d"x)/(1 + cos x)`

= `int 1/(2 cos^2  x/2) "d"x`

= `1/2 int sec^2  x/2 "d"x`

= `1/2 * 1/(1/2) tan  x/2 + "C"`

= `tan  x/2 + "C"`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Exercise [पृष्ठ १६४]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate : `intsin(x-a)/sin(x+a)dx`

 


Find the integrals of the function:

sin 3x cos 4x


Find the integrals of the function:

cos 2x cos 4x cos 6x


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:

`(1-cosx)/(1 +  cos x)`


Find the integrals of the function:

tan4x


Find the integrals of the function:

`(cos 2x+ 2sin^2x)/(cos^2 x)`


Find the integrals of the function:

`1/(sin xcos^3 x)`


Find the integrals of the function:

`(cos 2x)/(cos x + sin x)^2`


`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.


`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.


Find  `int dx/(x^2 + 4x + 8)`


Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.


Evaluate `int_0^(3/2) |x sin pix|dx`


Find `int (2x)/((x^2 + 1)(x^4 + 4))`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_  (log "x")^2 d"x"`


Find: `int_  (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`


Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`


Find: `int sin^-1 (2x) dx.`


Find `int x^2tan^-1x"d"x`


`int "e"^x (cosx - sinx)"d"x` is equal to ______.


`int "dx"/(sin^2x cos^2x)` is equal to ______.


`int (sin^6x)/(cos^8x) "d"x` = ______.


Evaluate the following:

`int tan^2x sec^4 x"d"x`


Evaluate the following:

`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`


Evaluate the following:

`int sqrt(1 + sinx)"d"x`


Evaluate the following:

`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`


Evaluate the following:

`int sin^-1 sqrt(x/("a" + x)) "d"x`  (Hint: Put x = a tan2θ)


`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.


`int sinx/(3 + 4cos^2x) "d"x` = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×