Evaluate the integrals

${\int}_{-\frac{\pi}{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx$

emancipezN
2021-10-14
Answered

Evaluate the integrals

${\int}_{-\frac{\pi}{3}}^{0}\mathrm{sec}x\mathrm{tan}xdx$

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Laith Petty

Answered 2021-10-15
Author has **103** answers

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

Formula:

Calculation:

Write the define integral.

Therefore, the value of the definite integral

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e) The integral describes the volume of the solid obtained by rotating the region

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