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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
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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"`
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Integrals of Trignometric Functions
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