Volume benda putar yang terjadi jika daerah yang terletak di kuadran I dan dibatasi oleh kurva y = x^2 garis y = 2x, diputar 360° terhadap sumbu x adalah
fatihahalhusna
![Dari\ grafik:\\\\\displaystyle V= \pi\int\limits^2_0 {[(2x)^2-(x^2)^2]} \, dx\\\\~~~= \pi\int\limits^2_0 {4x^2-x^4} \, dx \\\\~~~=\pi(\dfrac{4}{3}x^3-\left\dfrac{1}{5}x^5)\right]_0^2\\\\~~~=\pi(\dfrac{32}{3}-\dfrac{32}{5})\\\\~~~=\boxed{\boxed{\bold{\dfrac{64}{15}\pi}}}](https://tex.z-dn.net/?f=Dari%5C+grafik%3A%5C%5C%5C%5C%5Cdisplaystyle+V%3D+%5Cpi%5Cint%5Climits%5E2_0+%7B%5B%282x%29%5E2-%28x%5E2%29%5E2%5D%7D+%5C%2C+dx%5C%5C%5C%5C%7E%7E%7E%3D+%5Cpi%5Cint%5Climits%5E2_0+%7B4x%5E2-x%5E4%7D+%5C%2C+dx+%5C%5C%5C%5C%7E%7E%7E%3D%5Cpi%28%5Cdfrac%7B4%7D%7B3%7Dx%5E3-%5Cleft%5Cdfrac%7B1%7D%7B5%7Dx%5E5%29%5Cright%5D_0%5E2%5C%5C%5C%5C%7E%7E%7E%3D%5Cpi%28%5Cdfrac%7B32%7D%7B3%7D-%5Cdfrac%7B32%7D%7B5%7D%29%5C%5C%5C%5C%7E%7E%7E%3D%5Cboxed%7B%5Cboxed%7B%5Cbold%7B%5Cdfrac%7B64%7D%7B15%7D%5Cpi%7D%7D%7D "Dari\ grafik:\\\\\displaystyle V= \pi\int\limits^2_0 {[(2x)^2-(x^2)^2]} \, dx\\\\~~~= \pi\int\limits^2_0 {4x^2-x^4} \, dx \\\\~~~=\pi(\dfrac{4}{3}x^3-\left\dfrac{1}{5}x^5)\right]_0^2\\\\~~~=\pi(\dfrac{32}{3}-\dfrac{32}{5})\\\\~~~=\boxed{\boxed{\bold{\dfrac{64}{15}\pi}}}")
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patriaprastika
wah
fatihahalhusna
gambar grafiknya pakai software geogebra gratis kok...
patriaprastika
Sip pak, nanti saya coba. Makin keren aja jadi jawabannya
fatihahalhusna
Ia kemarin mau bilang tapi lupa aja... hehehe
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