English

D∫cosx1+sinxdx = ______.

Advertisements
Advertisements

Question

`int cosx/sqrt(1 + sinx) "d"x` = ______.

Options

  • `sin (x/2) - cos (x/2) + "c"`

  • `sin (x / 2) + cos (x/2) + "c"`

  • `2[sin(x/2) - cos(x/2)] + "c"`

  • `2[sin(x/2) + cos(x/2)] + "c"`

MCQ
Fill in the Blanks
Advertisements

Solution

`int cosx/sqrt(1 + sinx) "d"x` = `2[sin(x/2) + cos(x/2)] + "c"`.

Explanation:

`int cosx/sqrt(1 + sinx) "d"x = 2sqrt(1 + sinx) + "c"`  ......`[because int ("f'"(x))/sqrt("f"(x)) "d"x = 2sqrt("f"(x)) + "c"]`

= `2sqrt((sin  x/2 + cos  x/2)^2) + "c"`

= `2[sin(x/2) + cos(x/2)] + "c"`

shaalaa.com
Integrals of Trignometric Functions
  Is there an error in this question or solution?
Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×