Mathematics, 15.10.2019 08:30 shanua
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.
Answers: 1
![4-x^2=x\\ x^2+x-4=0\\ \Delta=1^2-4\cdot1\cdot(-4)=1+16=17\\ x_1=\dfrac{-1-\sqrt{17}}{2}\\ x_2=\dfrac{-1+\sqrt{17}}{2}\\\\ \displaystyle V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(4-x^2-x)^2\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(16-4x^2-4x-4x^2+x^4+x^3-4x+x^3+x^2)\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(x^4+2x^3-7x^2-8x+16)\,dx\\ V=\pi \left[\dfrac{x^5}{5}+\dfrac{x^4}{2}-\dfrac{7x^3}{3}-4x^2+16x\right]_0^{\dfrac{-1+\sqrt{17}}{2}}\\ ](/tpl/images/0321/3410/c79f2.png)
Another question on Mathematics
Mathematics, 21.06.2019 20:00
Consider the set of all four-digit positive integers less than 2000 whose digits have a sum of 24. what is the median of this set of integers?
Answers: 1
Mathematics, 21.06.2019 23:40
From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. if the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.
Answers: 1
Mathematics, 22.06.2019 01:10
You work in a hospital that has 9 floors. you need to see 3 patients on each floor. how many patients do you need to see in all?
Answers: 2
You know the right answer?
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved a...
Questions
English, 20.06.2019 18:02
Mathematics, 20.06.2019 18:02
History, 20.06.2019 18:02
Health, 20.06.2019 18:02
Mathematics, 20.06.2019 18:02
History, 20.06.2019 18:02
Mathematics, 20.06.2019 18:02
World Languages, 20.06.2019 18:02
Biology, 20.06.2019 18:02
