Answer
Area $=\displaystyle \int_{0}^{\pi/4}\tan xdx$
Work Step by Step
Th. 4.5 The Definite lntegral as the Area of a Region
If $f$ is continuous and nonnegative on the closed interval $[a, b]$,
then the area of the region bounded by
the graph of $f$,
the x-axis, and
the vertical lines $x=a$ and $x=b$ is
Area $=\displaystyle \int_{a}^{b}f(x)dx$.
(See Figure 4.22.)
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$[a, b]$ = $[0,\pi/4]$
$f(x)=\tan x$ is continuous and nonnegative on the interval,
(just the setup:)
Area $=\displaystyle \int_{0}^{\pi/4}\tan xdx$
