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Evaluate int(0)^(2pi)|cosx|dx...

Evaluate `int_(0)^(2pi)|cosx|dx`

Text Solution

Verified by Experts

Let's break the integral as below :
`int_(0)^(2pi)|cosx|dx=int_(0)^((pi)/(2))|cosx|dx+int_(0)^((3pi)/(2))|cosx|dx+int_((3pi)/(2))^(2pi)|cosx|dx`
`=int_(0)^((pi)/(2))cosxdx-int_((pi)/(2))^((3pi)/(2))cosxdx+int_((3pi)/(2))^(2pi)cosxdx`
(We can found out the intervals in which `cosx` in positive or `cosx` is negative)
`=[sinx]_(0)^(pi//2)-[sinx]_(pi//2)^(3pi//2)+[sinx]_(3pi//2)^(2pi)`
`=(1-0)-[-1-1]+[0-(-1)]`
`=1+2+1`
`=4`
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int_(0)^(2pi)|cosx|dx=4

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Knowledge Check

  • int_(0)^(2pi)(sinx+cosx)dx=

    A
    0
    B
    2
    C
    -2
    D
    1
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