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Question
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
Options
0
2
π
1
Solution
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is π.
Explanation:
Let `int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1)` dx
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x) dx + int_((-pi)/2)^(pi/2) 1* dx`
Because `(x^3 + x cos x + tan^5 x)` is an equivalent function.
Hence, `int_(-pi//2)^(pi//2) (x^3 + x cos x + tan^5 x) dx = 0`
`=> I = 0 + [x]_(-pi/2)^(pi/2)`
`= pi/2 - (- pi/2)`
`= pi/2 + pi/2 = pi`
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