Volume of solid Definition and 73 Threads

Homework Statement Find the volume of the solid formed by rotating the region enclosed by the following equations about the Y-AXIS. y= e^(3x)+5 y=0 x=0 x= 1/2 Homework Equations The Attempt at a Solution I keep getting the answer wrong. I broke the problem into two parts: solved a...

Homework Statement Sketch the solid E bounded by the cylinder x = y^2 and the planes z = 3 and x + z = 1, and write down its analytic expression. Then, use a triple integral to find the volume of E. The Attempt at a Solution Was wondering if someone could have a go at drawing this sketch...

Homework Statement f(x) =e^x and g(x)= ln(x) Find the volume of the solid generated when the region enclosed by the graphs of f and g between x=1/2 and x=1 is revolved about the line y=4 Homework Equations v= pi* integral( f(x)^2 - g(x)^2 dx) The Attempt at a Solution SO for...

Hello folks, I was wondering how to set up a volume of the solid of revolution about a line in the form of a line equation. if i wanted to find the volume about a line of x/4 would I simply find it as v=pi*integral (f(x/4)^2)dx or is there a method I'm missing all togeather?

Find the volume of the solid under the graph of z=sqrt(16-x^2-y^2) and above the circular region x^2+y^2<=4 in the xy plane I know I must go to polar. So z=sqrt(16-r^2). Does r range from 0-2? I am not sure what theta ranges from (0-2pi)? I set up the integral as int(int r*sqrt(16-r^2)...

Hello ppl. I have a problem in finding out the volume of solid formed by the revolution of one loop of lemniscate of bernoulli ( r²=a²cos2θ) about the initial line θ =0 Using the relevant forumula for the volume of the solid generated by the revolution of one loop of the polar curve about the...

Homework Statement Find the volume V of the solid bounded by the graph x2+y2=9 and y2+z2=9 Homework Equations The Attempt at a Solution When I started this problem, I thought it was a perfect sphere with the center points (0, 0, 0). And then I thought, "Why do I need calculus, it's...

volume of the torus, by revolving around line x = 3 inside circle x^2 + y^2 = 4 i got x = sqrt(y^2 - 4) and what would v = ?

Homework Statement y = x³ y= 0 and x = 1 and its revolved around the line x = 2 okay i have drawn the graph of y = x³ and other paramaters, but when i get ther area being rotated it produces a hollow center. how do i go about finding the volume? would it be a washers i don't...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the graph of y = x3 and the line y = x, between x = 0 and x = 1, about the y-axis. Homework Equations \pi\overline{1}\int\underline{0}[R(x)^{2}-[r(x)]^{2}dx The Attempt at a Solution...

Homework Statement Find the volume of a solid formed by revolving the region bounded by graphs of: y=x^3 y=1 and x=2 Homework Equations \pi0\int2(x^3)dx The Attempt at a Solution x^7/7 with boundaries of [0,2] Am I on the right path?

Homework Statement Find the volume of the solid of revolution: F(x)=2x+3 on [0,1] Revolved over the line x=3 and y=5 Homework Equations Shell Method: 2\pi\int^{b}_{a}x[f(x)-g(x)]dx obviously just sub y for dy Disk Method: /pi/int^{b}_{a}[F(x)^{2}-G(x)^{2}dx

find the volume of the solid resulting when the region enclosed by the curves is revolved around y-axis. x=\sqrt{1+y} x=0 y=3 I am using this integral... V=\int_{-1}^3[\pi(\sqrt{1+y})^2]dy and I am getting the wrong answer. I think it is just arithmetic, but are my bounds...

Ok, I'm supposed to found the volume of the solid that is created after rotating the line f(x) = 2x-1 around the x axis. The limits are y=0 x=3 and x=0. I've been trying for about and hour, and keep getting the answer: 46.0766. I've done the integration tons of times, splitting the problem...

volume of solid:( hi..I tried to solve it but ı couldn't .book says the answer is pi /6...please help me. question is; y=x and y=x^1/2 about y =1

so i have one problem and i just need to know if my integral is right. any help would be greatly appreciated 1. a ball of radius 10 has a round hole of radius 5 drilled through its center. find the volume of the resulting solid. i know volume of cylinder removed is pi*5^2*10*sqrt(3) because...

Hi Could someone please give me an idea on how to go about this problem Find the volume of the curve genereated by revolving the area between the curve y =(cos x)/x and the x-axis in the interval pie/6 to pie/2 Thanks a lot..

Here is the problem: Find the volume of the solid that is bounded above by the cylinder z = 4 - x^2, on the sides by the cylinder x^2 + y^2 = 4, and below by the xy-plane. Here is what I have: \int_{-2}^{2}\int_{-\sqrt{4 - x^2}}^{\sqrt{4 - x^2}}\int_{0}^{4 - x^2}\;dz\;dy\;dx\;=\;12\pi...

"simple" shell I know this is relatively simple, but I'm a little rusty. Could someone help me out? We want to find the volume of the solid obtained by rotating the region bounded by the curves y=x^4 and y=1 about the line y=7 using the cylindrical shell method. According to my book the...

The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid? How come the answer isn't just the intgegral from 0-8 of 1/2pi(4-x/2)^2

Hello, I am still unsure of my ability to evaluate the volume of a solid using triple integrals. Here is my question: Now I know that the intersection of the two paraboloids is 9 = x^2 + y^2. But I am unsure how to set up the triple integral. I was thinking of splitting the volume...

Hello, I am having trouble setting up triple integrals to find a volume of a given solid. Here is one of the questions with which I am having trouble. Now I can see that the projection of the solid on the xy plane is the circle x^2 + y^2 = 9. And I think I can visualize the plane z = y +...

The quadrant of the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2} = 1. lying in the first quadrant, revolves about the line joining the extremities of the major and minor axis. Show that the volume of the solid generated is \frac{\pi a^2 b^2}{\sqrt{a^2+b^2}} (\frac{5}{3} - \frac{\pi}{2}). I tried...