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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
4.7
95 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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