Homework Statement
Let l, w, and h be the length, width and height of a rectangular box. The length l is increasing with time at at rate of 1 m/s, while the width and the height are decreasing at rates 2 m/s and 1m/s respectively. At a certain moment in time the dimensions of the box are l=5...
Homework Statement
Evaluate
Integrate (2-3x/(Sqrt.(1 - x^2))) dx
Homework Equations
1/Sqrt.(1-x^2) = arctan
The Attempt at a Solution
I am so lost, but this is what I've tried, but didn't work...
I separated the integral into two so
Integral of (2/(Sqrt.(1-x^20))) dx - integral of...
So this was also given in the problem, which I forgot to mention.
a) Note that x^n(t)=8; then use Newton's second law (F= ma = mx^n(t)) to evaluate the work integral.
(Given)
F= ma = mx^n(t))
x^n(t)=8
F= (2)(8)
F=16
W = Integral of F(x)dx from 0 to 5
I integrated 16x from 0 to 5 and got...
Homework Statement
a rigid body with a mass of 2 kg moves along a line due to a force that produces a position function x(t)= 4t^2, where x is measured in meters and t is measured in seconds. Find the work done during the first 5 seconds in two ways.
Homework Equations
x(t)= 4t^2
Work is ->...
Homework Statement
Find the region bounded by y= 2x and y = x^2 + 3x - 6.
I found the points of intersection to be x= -3, 2 by setting the equations equal to each other and solving for x.
I concluded that y = x^2+3x-6 is bigger since I tried a point in between the points of intersection and it...
Find the area of the regions shown in the figures.
These are the graphs used :
y = x^2
x = 2 Sin ^2 (y)
I know that I need to set the two equations equal to each other in order to find the points of intersection, but I run into some trouble when trying to simplify it for y.
This is what...