English

Find the integrals of the function: sin2x1+cosx

Advertisements
Advertisements

Question

Find the integrals of the function:

`(sin^2 x)/(1 + cos x)`

Sum
Advertisements

Solution

Let `I = int (sin^2 x)/(1 + cos x)  dx`

= `int (1 - cos^2 x)/(1+ cos x)  dx`

= `int ((1 - cos x) (1 + cos x))/(1 + cos x)  dx`

= `int (1 - cos x) dx`

= `int 1  dx - int cos x  dx`

= x - sin x + C

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.3 [Page 307]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.3 | Q 12 | Page 307

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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:

`(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:

`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`


Find the integrals of the function:

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


Find the integrals of the function:

sin−1 (cos 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_  sin ("x" - a)/(sin ("x" + a )) d"x"`


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


Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.


Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`


Find `int "dx"/(2sin^2x + 5cos^2x)`


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


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


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


Evaluate the following:

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


Evaluate the following:

`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`


The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4  dx` is


`int (cos^2x)/(sin x + cos x)^2  dx` is equal to


Which identity is used for \(\cos^2 x\)?


Which identity is used for an even power of cosine?


Which identity is used for the product of sine and cosine?


What is \(\int \cos^2 x\,dx\)?


What is \(\int \sin 2x\cos 3x\,dx\)?


Which procedure is recommended when an identity can simplify a complicated trigonometric expression?


After a trigonometric expression has been simplified, how should it be integrated?


What must always be added to an indefinite integral?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×