![V=\pi\cdot\int\limits_0^9(x^3)^2\, dx=\pi\cdot\int\limits_0^9x^6\, dx=\pi\cdot\left[\dfrac{x^7}{7}\right]_0^9=\pi\cdot\left(\dfrac{9^7}{7}-\dfrac{0^7}{7}\right)=\dfrac{9^7}{7}\pi=\\\\\\=\boxed{\dfrac{4782969}{7}\pi}](/tpl/images/0447/3301/56d48.png)
![V=2\pi\cdot\int\limits_0^{9}(x\cdot x^3)\, dx=2\pi\cdot\int\limits_0^{9}x^4\, dx= 2\pi\cdot\left[\dfrac{x^5}{5}\right]_0^9=2\pi\cdot\left(\dfrac{9^5}{5}-\dfrac{0^5}{5}\right)=\\\\\\=2\pi\cdot\dfrac{9^5}{5}=\boxed{\dfrac{118098}{5}\pi}](/tpl/images/0447/3301/89975.png)
![V=2\pi\cdot\int\limits_0^9\big((18-x)\cdot x^3\big)\, dx=2\pi\cdot\int\limits_0^9(18x^3-x^4)\, dx=\\\\\\=2\pi\cdot\left(\int\limits_0^918x^3\, dx-\int\limits_0^9x^4\, dx\right)=2\pi\cdot\left(18\int\limits_0^9x^3\, dx-\int\limits_0^9x^4\, dx\right)=\\\\\\=2\pi\cdot\left(18\left[\dfrac{x^4}{4}\right]_0^9-\left[\dfrac{x^5}{5}\right]_0^9\right)=2\pi\cdot\Biggl(18\biggl(\dfrac{9^4}{4}-\dfrac{0^4}{4}\biggr)-\biggl(\dfrac{9^5}{5}-\dfrac{0^5}{5}\biggr)\Biggr)=\\\\\\](/tpl/images/0447/3301/497ac.png)
99 point question, plus !
( answer genuinely, and do not answer just for points, if you do, y...
Mathematics, 08.01.2020 21:31 kim643
99 point question, plus !
( answer genuinely, and do not answer just for points, if you do, your answer will be deleted, and those points will be taken
this is calculus not basic
10.) use the disk or shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given line.
y = x^3, y = 0, x = 9
(i) the x-axis; (ii) the y-axis; (iii) the line x = 18
a • (i) 9565958/7 pi (ii) 118098/5 pi (iii) 177147/5 pi
b • (i) 4782969/7 pi (ii) 59049/5 pi (iii) 177147/5 pi
c • (i) 9565958/7 pi (ii) 118098/5 pi (iii) 118098/5 pi
d • (i) 4782969/7 pi (ii) 118098/5 pi (iii) 177147/5 pi
** show all of you work, if you do not, your answer will be deleted, and the points you earned will be taken
Answers: 3
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