Integrate the function sin(x)/(cos(x)^2) from -pi/4 to pi/4

 Exercise

$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)^2}\right)dx$

 

Simplify $\frac{\sin\left(x\right)}{\cos\left(x\right)^2}$ into $\tan\left(x\right)\sec\left(x\right)$ by applying trigonometric identities

$\int_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\tan\left(x\right)\sec\left(x\right)dx$

 

Apply the formula: $\int\sec\left(\theta \right)\tan\left(\theta \right)dx$$=\sec\left(\theta \right)+C$

$\left[\sec\left(x\right)\right]_{-\frac{\pi }{4}}^{\frac{\pi }{4}}$

 

Evaluate the definite integral

$\sec\left(\frac{\pi }{4}\right)-\sec\left(-\frac{\pi }{4}\right)$

$\sec\left(\frac{\pi }{4}\right)-\sec\left(-\frac{\pi }{4}\right)$

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