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The value of int(-pi/2)^(pi/2)(x^3+xco...

The value of `int_(-pi/2)^(pi/2)(x^3+xcosx+tan^5x+1)dx`

Text Solution

Verified by Experts

The correct Answer is:
C
`"Let I "= int_(-(pi)/(2))^(pi//2) (x^(3) +x cos x+ tan^(5) x+1)dx`
`rArr I= int_(-pi//2)^(pi//2) x^(3) dx+ int_((-pi)/(2))^(pi//2) x cos x dx`
`+int_((-pi)/(2))^(pi//2) tan^(5) x dx +int_((-pi)/(2))^(pi//2) 1 dx`
we know that
`int_(-a)^(a) f(x) dx={ 2int_(0)^(a) f(x) dx, " if " f(x) " is even "`
`0" ""if " f(x) " is odd"`
`:. " "I= 0+0+0+2 int_(0)^(pi//2) 1 dx`
`[ :' x^(3) x cos x " and "tan^(5) (x) " are odd function "]`
`I=2[x]_(0)^(pi//2) =(2pi)/(2)=pi`
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