Shell Method -I need an urgent help!
- Thread starter elfinitty
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- Feb 4, 2004
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This is my best guess as to the text within the first of your images:
26) Find the vol. of the sol. [??] by revolving the region in the first quadrant bounded on left by the curve x2 + y2 = 3 or the right by the line \(\displaystyle \, \lambda\, =\, \sqrt{3\,}\) and above by the line \(\displaystyle \, y\, =\, \sqrt{3\,}\,\) about(2) the y-axis (b) the x-axis using wosher and shell methal.
washer method.
\(\displaystyle v\, =\, \Pi\, \displaystyle{\int_0^{\sqrt{3\,}}}\, \dfrac{\left(\sqrt{3\,}\right)^2}{R^2(y)}\, -\, \dfrac{\left(\sqrt{3\, -\, y^2\,}\right)^L}{r^2(y)}\, dy\)
\(\displaystyle u\, =\, \pi\, \displaystyle{\int_0^{\sqrt{3\,}}}\, \left(3\, -\, 3\, +\, y^2\right)\, dy\, =\, \pi\, \cdot\, \dfrac{y^3}{3}\,\) \(\displaystyle \,\displaystyle{\int_d^{r_3}}\, =\, \dfrac{3r_3}{3}\, =\, r_3\, \pi\)
Kindly please forgive whatever errors I must have made, and reply with corrections and clarifications. Thank you!
26) Find the vol. of the sol. [??] by revolving the region in the first quadrant bounded on left by the curve x2 + y2 = 3 or the right by the line \(\displaystyle \, \lambda\, =\, \sqrt{3\,}\) and above by the line \(\displaystyle \, y\, =\, \sqrt{3\,}\,\) about(2) the y-axis (b) the x-axis using wosher and shell methal.
washer method.
\(\displaystyle v\, =\, \Pi\, \displaystyle{\int_0^{\sqrt{3\,}}}\, \dfrac{\left(\sqrt{3\,}\right)^2}{R^2(y)}\, -\, \dfrac{\left(\sqrt{3\, -\, y^2\,}\right)^L}{r^2(y)}\, dy\)
\(\displaystyle u\, =\, \pi\, \displaystyle{\int_0^{\sqrt{3\,}}}\, \left(3\, -\, 3\, +\, y^2\right)\, dy\, =\, \pi\, \cdot\, \dfrac{y^3}{3}\,\) \(\displaystyle \,\displaystyle{\int_d^{r_3}}\, =\, \dfrac{3r_3}{3}\, =\, r_3\, \pi\)
Kindly please forgive whatever errors I must have made, and reply with corrections and clarifications. Thank you!