Perhatikan perhitungan berikut ini
Untuk membuat grafik persamaan garis
dan
maka cari terlebih dahulu perpotongan dengan sumbu-X dan sumbu-Y perpotongan kedua persamaan tersebut.
Persamaan
berpotongan dengan sumbu-X, maka
:
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative x squared plus 4 x end cell row 0 equals cell negative x squared plus 4 x end cell row cell x squared minus 4 x end cell equals 0 row cell x open parentheses x minus 4 close parentheses end cell equals 0 end table end style](data:image/png;base64,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)
Maka
atau
. Didapatkan
dan
.
Persamaan
berpotongan dengan sumbu-Y, maka
:
![begin mathsize 14px style y equals negative x squared plus 4 x y equals negative open parentheses 0 close parentheses squared plus 4 open parentheses 0 close parentheses y equals 0 end style](data:image/png;base64,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)
Didapatkan
.
Persamaan
berpotongan dengan sumbu-Y, maka
maka didapatkan
, dan sebaliknya. Jika nilai
, maka nilai
didapatkan
, jika
maka nilai
didapatkan
dan seterusnya, maka akan membentuk grafik melengkung terbuka ke atas.
Perpotongan kedua persamaan tersebut, yaitu:
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals y row cell x squared end cell equals cell negative x squared plus 4 x end cell row cell x squared plus x squared minus 4 x end cell equals 0 row cell 2 x squared minus 4 x end cell equals 0 row cell x squared minus 2 x end cell equals 0 row cell x open parentheses x minus 2 close parentheses end cell equals 0 end table end style](data:image/png;base64,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)
Maka
atau
, masukan
ke persamaan
didapatkan
sehingga
.
Grafik kedua persamaan tersebut yaitu:
![](https://imgix2.ruangguru.com/assets/miscellaneous/jpg_gkh36s_9163.JPG)
Untuk mencari luas yang dibatasi sumbu-X dan sumbu-Y, maka luas daerah yang didapatkan:
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_pbydjh_5488.png)
Untuk mencari luas daerah yang diarsir maka dapat menggunakan konsep integral dengan batas
sampai
, sehingga:
Luas===========∫abf(x)−g(x)∫02−x2+4x−(x2)∫02−x2+4x−x2∫02−2x2+4x[−32x3+24x2]02[−32x3+2x2]02[−32(2)3+2(2)2−(−32(0)3+2(0)2)]−316+8−03−16+24382,67
Jadi, luas daerah yang diarsir adalah
.