Daerah yang dibatasi oleh kurva 
dan garis x=9 dibagi oleh garis x=c (c>0) menjadi dua daerah dengan luas sama. Tentukan nilai c.
Takamori37
Sesuaikan batas, akan diperoleh pengintegralan:
![$\begin{align}L_I&=L_{II} \\ \int_0^c\sqrt x\, dx&=\int_c^9\sqrt x\, dx \\ \int_0^cx^{1/2}\, dx&=\int_c^9x^{1/2}\, dx \\ \left.\frac1{3/2}x^{3/2}\right]_0^c&=\left.\frac1{3/2}x^{3/2}\right]_c^9 \\ \frac23(c^{3/2}-0^{3/2})&=\frac23(9^{3/2}-c^{3/2}) \\ c^{3/2}-0&=27-c^{3/2} \\ 2c^{3/2}&=27 \\ c^{3/2}&=\frac{27}2 \\ c&=\sqrt[3]{\left[\frac{27}2\right]^2} \\ c&=\frac{9}{\sqrt[3]{4}} \\ c&\approx 5,67\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7DL_I%26%3DL_%7BII%7D+%5C%5C+%5Cint_0%5Ec%5Csqrt+x%5C%2C+dx%26%3D%5Cint_c%5E9%5Csqrt+x%5C%2C+dx+%5C%5C+%5Cint_0%5Ecx%5E%7B1%2F2%7D%5C%2C+dx%26%3D%5Cint_c%5E9x%5E%7B1%2F2%7D%5C%2C+dx+%5C%5C+%5Cleft.%5Cfrac1%7B3%2F2%7Dx%5E%7B3%2F2%7D%5Cright%5D_0%5Ec%26%3D%5Cleft.%5Cfrac1%7B3%2F2%7Dx%5E%7B3%2F2%7D%5Cright%5D_c%5E9+%5C%5C+%5Cfrac23%28c%5E%7B3%2F2%7D-0%5E%7B3%2F2%7D%29%26%3D%5Cfrac23%289%5E%7B3%2F2%7D-c%5E%7B3%2F2%7D%29+%5C%5C+c%5E%7B3%2F2%7D-0%26%3D27-c%5E%7B3%2F2%7D+%5C%5C+2c%5E%7B3%2F2%7D%26%3D27+%5C%5C+c%5E%7B3%2F2%7D%26%3D%5Cfrac%7B27%7D2+%5C%5C+c%26%3D%5Csqrt%5B3%5D%7B%5Cleft%5B%5Cfrac%7B27%7D2%5Cright%5D%5E2%7D+%5C%5C+c%26%3D%5Cfrac%7B9%7D%7B%5Csqrt%5B3%5D%7B4%7D%7D+%5C%5C+c%26%5Capprox+5%2C67%5Cend%7Balign%7D "$\begin{align}L_I&=L_{II} \\ \int_0^c\sqrt x\, dx&=\int_c^9\sqrt x\, dx \\ \int_0^cx^{1/2}\, dx&=\int_c^9x^{1/2}\, dx \\ \left.\frac1{3/2}x^{3/2}\right]_0^c&=\left.\frac1{3/2}x^{3/2}\right]_c^9 \\ \frac23(c^{3/2}-0^{3/2})&=\frac23(9^{3/2}-c^{3/2}) \\ c^{3/2}-0&=27-c^{3/2} \\ 2c^{3/2}&=27 \\ c^{3/2}&=\frac{27}2 \\ c&=\sqrt[3]{\left[\frac{27}2\right]^2} \\ c&=\frac{9}{\sqrt[3]{4}} \\ c&\approx 5,67\end{align}")
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