Question

Find the positive value of k such that the area of the region enclosed between the graph y=kcosx and the graph y=kx^2 is 2

Answer 1

The student's question requires finding the value of 'k' that makes the enclosed area between two curves equal to 2. Without specified integration limits, we can't provide an exact solution, but the question generally involves setting up an integral to solve for 'k'.

Step-by-step explanation:

The student has asked to find the positive value of k such that the area of the region enclosed between the graph y=kcosx and the graph y=kx^2 is 2. To solve this problem, we generally need to set up an integral that represents the area between the two curves and solve for k. However, without additional information about the limits of integration or a more explicit connection to the oscillating function and spring dynamics mentioned in the supporting information, we cannot provide a specific solution. The supporting information hints at a mathematical model of physical systems involving harmonic motion or wave functions, but it is not directly applicable to the problem presented without further context.

Answer 2

Both these graphs will pass through the origin so you need to work out the difference in areas by integrating

INtegral k cos x (between the limits 0 and a) - Intgral kx^2 ( between 0 and a) = 2
Find k
(where a is the value of x on positive side of the graph where the 2 curves intersect)