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SMK Teknologi dan Rekayasa

Soal 127 Luas Daerah antara Dua Kurva


Luas\ daerah\ yang\ dibatasi\ oleh\ parabola\ y=8-x^{2}\ dan\ garis\ y=2x\\adalah\ ....\\ \\a.\ \ 36\ satuan\ luas\\ \\b.\ \ 41\frac{1}{3}\ satuan\ luas\\ \\c.\ \ 41\frac{2}{3}\ satuan\ luas\\ \\d.\ \ 46\ satuan\ luas\\ \\e.\ \ 46\frac{2}{3}\ satuan\ luas
Jawaban: a

Seperti\ jawaban\ soal\ 126,\ tetapi\ kali\ ini\ penulis\ menunjukkan\\\mathbf{trik\ jitu}nya\ saja.
\mathbf{Trik\ jitu}:
y_{1}=8-x^{2}\ \ \ \ \ \ \ y_{2}=2x
y_{1}-y_{2}=8-x^{2}-2x=-x^{2}-2x+8
a=-1,\ b=-2,\ c=8
Diskriminan:\ \ \ D=b^{2}-4ac=(-2)^{2}-4(-1).8=4+32=36
\begin{array}{rcl}Luas\ daerah&=&\frac{D\sqrt{D}}{6a^{2}}\\\\&=&\frac{36\sqrt{36}}{6.(-1)^{2}}\\\\&=&\frac{36\times 6}{6.1}\\\\&=&36\end{array}

About Kalakay

Guru Matematika SMK

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