Question

If $f\left(x\right)=\frac{x^7-3x^5+7x^3-x+1}{{\cos }^{2}x}$ then ${\int }_{-\pi /4}^{\pi /4}f\left(x\right)dx$ is equals to

• A. $\frac{\pi }{2}$
• B. $0$
• C. $2$
• D. ${\int }_0^{\pi /4}f\left(x\right)dx$

Answer 1

The correct option is C $2$

$f\left(x\right)=\frac{x^7-{3x}^5+{7x}^3-x+1}{{\cos }^{2}x}$

${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}f\left(x\right)dx\{\because f\left(x\right)=-f(-x)\}$

$={\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}\frac{dx}{{\cos }^{2}x}$

$={\left(tanx\right)}_{-\pi /4}^{\pi /4}=2$