Volume benda putar yang di batasi kurva y=akar x garis x=1 dan garis x=4 di putar mengelilingi sumbu x sejauh 360 derajat adalah..
Rieaz
![y= \sqrt{x}, y^2=x \\ a = 4, b = 1 \\ = \int\limits^a_b {y^2} \, dx \\ = \int\limits^4_1 {x} \, dx \\ = \frac{1}{2}x^2 \left \{ {{a=4} \atop {b=1}} \right. \\ =[(\frac{1}{2}4^2)-(\frac{1}{2}1^2)] \\ =[8-\frac{1}{2}] \\ =7\frac{1}{2} atau\frac{15}{2}](https://tex.z-dn.net/?f=y%3D+%5Csqrt%7Bx%7D%2C+y%5E2%3Dx++%5C%5C+a+%3D+4%2C++b+%3D+1+%5C%5C+%3D++%5Cint%5Climits%5Ea_b+%7By%5E2%7D+%5C%2C+dx++%5C%5C+%3D+%5Cint%5Climits%5E4_1+%7Bx%7D+%5C%2C+dx++%5C%5C+%3D+%5Cfrac%7B1%7D%7B2%7Dx%5E2++%5Cleft+%5C%7B+%7B%7Ba%3D4%7D+%5Catop+%7Bb%3D1%7D%7D+%5Cright.++%5C%5C+%3D%5B%28%5Cfrac%7B1%7D%7B2%7D4%5E2%29-%28%5Cfrac%7B1%7D%7B2%7D1%5E2%29%5D+%5C%5C+%3D%5B8-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%3D7%5Cfrac%7B1%7D%7B2%7D++atau%5Cfrac%7B15%7D%7B2%7D "y= \sqrt{x}, y^2=x \\ a = 4, b = 1 \\ = \int\limits^a_b {y^2} \, dx \\ = \int\limits^4_1 {x} \, dx \\ = \frac{1}{2}x^2 \left \{ {{a=4} \atop {b=1}} \right. \\ =[(\frac{1}{2}4^2)-(\frac{1}{2}1^2)] \\ =[8-\frac{1}{2}] \\ =7\frac{1}{2} atau\frac{15}{2}")
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