# Evaluate the integrals \int_{-\pi/3}^0\sec x\tan xdx

Evaluate the integrals
${\int }_{-\frac{\pi }{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx$
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Laith Petty
Given information:
${\int }_{-\frac{\pi }{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx$
Formula:
$\mathrm{sec}x\mathrm{tan}xdx=\mathrm{sec}x$
Calculation:
Write the define integral.
${\int }_{\frac{-\pi }{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx={\left[\mathrm{sec}x\right]}_{\frac{-\pi }{3}}^{0}$
$=\mathrm{sec}0-\mathrm{sec}\left(\frac{-\pi }{3}\right)$
$=1-2$
$=-1$
Therefore, the value of the definite integral ${\int }_{-\frac{\pi }{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx$ is -1