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Evaluate: int(-pi/4)^(pi/4)(x^9-3x^5+7x^...

Evaluate: `int_(-pi/4)^(pi/4)(x^9-3x^5+7x^3-x+1)/(cos^2x)dx`

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Verified by Experts

`f(x)=(x^(9)-3x^(5)+7x^(3)-x)/(cos^(2)x+sec^(2)x)`
`sec^(2)x(x^(9)-3x^(5)+7x^(3)-x)+sec^(2)x`
`:.int_(pi//4)^(pi//4)f(x)dx=int_(-pi//4)^(pi//4)sec^(2) xdx`
`[ :' sec^(2)x(x^(9)-3x^(5)+7x^(3)-x)` is an odd function]
`=2int_(0)^(pi//4)sec^(2) xdx`
`=2[tanx]_(0)^(pi//4)=2`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
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