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anonymous
 4 years ago
Hey Guys I have some very hard math hw questions. I really have no idea how to start or anything. I am clueless.
1.)Sketch the region enclosed by the given curves. Find the area of the region y=sinx,y=sin2x,x=0, and x=pie/2
2.) Find the area bounded by the curves y=4(x squared) and y=2x+1.
3.) Find the volume of the solid obtained by rotating the region in #2 around the line x=2
4.)Let R be the region bounded by the graphs of y=square root of (x squared 9), y=0, x=3, and x=5. Compute the volume of the solid formed by revolving R about the y axis and x axis.
Please Help
anonymous
 4 years ago
Hey Guys I have some very hard math hw questions. I really have no idea how to start or anything. I am clueless. 1.)Sketch the region enclosed by the given curves. Find the area of the region y=sinx,y=sin2x,x=0, and x=pie/2 2.) Find the area bounded by the curves y=4(x squared) and y=2x+1. 3.) Find the volume of the solid obtained by rotating the region in #2 around the line x=2 4.)Let R be the region bounded by the graphs of y=square root of (x squared 9), y=0, x=3, and x=5. Compute the volume of the solid formed by revolving R about the y axis and x axis. Please Help

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.05.) the region R is enclosed by the curves y=x^2 and x=2y. Find the volume of this solid obtained by rotating the region about the line y=1. Thats the last question I need help on

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0use definite integrls to find area.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thats the problem idk what they are or where to begin. If someone could show me how to do one of them I could get the hang of it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I finally got numbers 1 and 2 but 35 have still stumped me

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.intmath.com/applicationsintegration/4volumesolidrevolution.php Here is how to you work out the volume. If you have any questions just ask :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i see how the website does it but then i try and im still lost lol.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay because the region is not being rotated around the xaxis we need to use the Washer Method. http://www.cliffsnotes.com/study_guide/VolumesofSolidsofRevolution.topicArticleId39909,articleId39907.html

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.03. \[Volume=\pi \int^b_a [f(x)]^2[g(x)]^2 dx\] From the diagram we see that the points will be 1 and 3 \[Volume=\pi \int^1_{3} (4x^2)^2(2x+1)^2 dx\]\[Volume=\pi \int^1_{3} 168x^2+x^44x^24x1dx\]\[Volume=\pi \int^1_{3} 1512x^2+x^44xdx\]\[Volume=\pi [ 15x4x^3+\frac{1}{5}x^52x^2]^1_{3}\]\[Volume=\pi [ (154+\frac{1}{5}2)(45+108\frac{243}{5}18)]\]\[Volume=\pi [ 8.8+3.6]\]\[Volume=\pi [12.4]\]\[Volume=\frac{62\pi}{5}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i wouldn't know the answer but it does look right. thanks zed a ton

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u used the exponent 2 because it s around x=2?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry that is the method you need to use for question 4.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For question 3 and 5, http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[y=4x^2 > x=\sqrt{4y}\] \[y=2x+1> x=\frac{y1}{2}\] Outer radius=4y+2=6y Inner radius =sqrt(4y)+2 So the crosssectional area is \[A(y)=\pi((6y)^2(\sqrt{4y}+2)^2)\]\[=y^211y4\sqrt{4y}+28\] Let this equal 0 to find where the first and final ring will occur. y=3 and y=4 Now we can calculate the volume \[V=\int^4_3 A(y) dy\]\[V=\pi\int^4_3 y^211y4\sqrt{4y}+28 dy\]\[V=\pi[\frac{1}{6}(16 (4  y)^{3/2} + 168 y  33 y^2 + 2 y^3)]^4_3\] Subbing in the values gives \[V=\frac{2749\pi}{60}\] Follow the method of the link I posted above to do question 5. Hope I haven't confused you. Good luck.
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