Integrate the function -sec(x)tan(x) from (-x)/4 to x/6

 Exercise

$\int_{-\frac{x}{4}}^{\frac{x}{6}}\left(-\sec\left(x\right)\tan\left(x\right)\right)dx$

 

The integral of a constant times a function is equal to the constant multiplied by the integral of the function

$-\int_{\frac{-x}{4}}^{\frac{x}{6}}\sec\left(x\right)\tan\left(x\right)dx$

 

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

$-\left[\sec\left(x\right)\right]_{\frac{-x}{4}}^{\frac{x}{6}}$

 

Evaluate the definite integral

$-\left(\sec\left(\frac{x}{6}\right)-\sec\left(\frac{-x}{4}\right)\right)$

$-\left(\sec\left(\frac{x}{6}\right)-\sec\left(\frac{-x}{4}\right)\right)$

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