Tentukan isi benda putar yang terjadi jika kurva y= x^{2}+1 di putar menggelilingi sumbu x sejauh 360°,sumbu x,sumbu y & garis x sama dengan 2? tlong ya jawabannaya :)
inoid
![\begin{array}{lcl} V&=&\pi\int\limits_0^2{y^2\,dx} \\ &=&\pi\int\limits_0^2{(x^2+1)^2\,dx} \\ &=&\pi\int\limits_0^2{x^4+2x^2+1\,dx} \\ &=&\pi\left[\frac15x^5+\frac23x^3+x\right]_0^2 \\ &=&\pi\left[\left(\frac15(2)^5+\frac23(2)^3+2\right)-0\right] \\ &=&\pi\left[\frac{32}5+\frac{16}3+2\right] \\ &=&\pi\left[\frac{96}{15}+\frac{80}{15}+\frac{30}{15}\right] \\ &=&\pi\left[\frac{206}{15}\right] \\ &=&\frac{206}{15}\pi \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcl%7D%0AV%26%3D%26%5Cpi%5Cint%5Climits_0%5E2%7By%5E2%5C%2Cdx%7D+%5C%5C%0A%26%3D%26%5Cpi%5Cint%5Climits_0%5E2%7B%28x%5E2%2B1%29%5E2%5C%2Cdx%7D+%5C%5C%0A%26%3D%26%5Cpi%5Cint%5Climits_0%5E2%7Bx%5E4%2B2x%5E2%2B1%5C%2Cdx%7D+%5C%5C%0A%26%3D%26%5Cpi%5Cleft%5B%5Cfrac15x%5E5%2B%5Cfrac23x%5E3%2Bx%5Cright%5D_0%5E2+%5C%5C%0A%26%3D%26%5Cpi%5Cleft%5B%5Cleft%28%5Cfrac15%282%29%5E5%2B%5Cfrac23%282%29%5E3%2B2%5Cright%29-0%5Cright%5D+%5C%5C%0A%26%3D%26%5Cpi%5Cleft%5B%5Cfrac%7B32%7D5%2B%5Cfrac%7B16%7D3%2B2%5Cright%5D+%5C%5C%0A%26%3D%26%5Cpi%5Cleft%5B%5Cfrac%7B96%7D%7B15%7D%2B%5Cfrac%7B80%7D%7B15%7D%2B%5Cfrac%7B30%7D%7B15%7D%5Cright%5D+%5C%5C%0A%26%3D%26%5Cpi%5Cleft%5B%5Cfrac%7B206%7D%7B15%7D%5Cright%5D+%5C%5C%0A%26%3D%26%5Cfrac%7B206%7D%7B15%7D%5Cpi%0A%5Cend%7Barray%7D "\begin{array}{lcl} V&=&\pi\int\limits_0^2{y^2\,dx} \\ &=&\pi\int\limits_0^2{(x^2+1)^2\,dx} \\ &=&\pi\int\limits_0^2{x^4+2x^2+1\,dx} \\ &=&\pi\left[\frac15x^5+\frac23x^3+x\right]_0^2 \\ &=&\pi\left[\left(\frac15(2)^5+\frac23(2)^3+2\right)-0\right] \\ &=&\pi\left[\frac{32}5+\frac{16}3+2\right] \\ &=&\pi\left[\frac{96}{15}+\frac{80}{15}+\frac{30}{15}\right] \\ &=&\pi\left[\frac{206}{15}\right] \\ &=&\frac{206}{15}\pi \end{array}")
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