How to do this integration question? (1 Viewer)

Silly Sausage · Mar 2, 2015

Just let the triangle be called $A$ ; semi-circle with Domain $1\leq{x}\leq3$ be called $B$ and the semi-circle with Domain $3\leq{x}\leq5$ called $C$ .
Let $h(x)=A+B+C$ where:
$\int^{1}_{-3}A\, dx=\frac{1}{2}(4)(2)=4$
$\int^{3}_{1}B\, dx=-\frac{(1)^{2}\pi}{2}$
$\int^{5}_{3}C\, dx=\frac{(1)^{2}\pi}{2}$
Thus, $\int^{5}_{-3}h(x)\, dx=\int^{5}_{-3}A+B+C\, dx$
$=4+-\frac{(1)^{2}\pi}{2}+\frac{(1)^{2}\pi}{2}=4$

For area, since it can't be negative:
$\int^{5}_{-3}\,h(x) dx=\int^{5}_{-3}A+|B|+C\, dx$
$4+|-\frac{(1)^{2}\pi}{2}|+\frac{(1)^{2}\pi}{2}=4+\pi$

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How to do this integration question? (1 Viewer)

Silly Sausage

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