Find the area of the region bounded by the graphs of the given functions y=tanx x=0 x=π/4

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Answer to a math question Find the area of the region bounded by the graphs of the given functions y=tanx x=0 x=π/4

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Esmeralda

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102 Answers

$=\int _{0}^{\frac{π}{4}}\frac{\sin(x)}{\cos(x)}dx$

$=\int _{1}^{\frac{\sqrt{2}}{2}}-\frac{1}{u}du$

$=-\int _{\frac{\sqrt{2}}{2}}^{1}-\frac{1}{u}du$

$=-(-\int _{\frac{\sqrt{2}}{2}}^{1}\frac{1}{u}du)$

$=-(-[\ln\left|u\right|]_{\frac{\sqrt{2}}{2}}^{1})$

$=[\ln\left|u\right|]_{\frac{1}{\sqrt{2}}}^{1}$

$=\frac{1}{2}\ln(2)$

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