The curves f(x) = 3-x^2 and g(x) = e^2x-1 are shown in the figure. Let R be the shaded region bounded by the graph if f(x), g(x) and the y axis. The vertical line x=k divides R into two regions where the area of the region to the left of the line x=k is 2/3 the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k. The image shows a graph with two curves intersecting on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -1 to 4.- The **red-shaded region** between the curves is labeled "R". This area represents the region bounded by the two curves.- The **blue curve** appears to start from approximately (x=-2, y=-0.5) and approaches the origin, increasing steeply towards the positive y-axis.- The **orange curve** starts near (x=-2, y=-0.5) and moves upwards, reaching a peak between x=0 and x=1, then descends, moving towards (x=2, y=-0.5).These curves could represent any mathematical functions, such as parabolas, with the shaded area indicating a region of integration or area of interest in calculus.

The given curves are and .Let be the shaded region bounded by the graph and the axis as shown below.Given that the vertical line divides into two regions where the area of the region to the left of the line is the area of the region to the right of the line.Therefore the region with line is drawn as follows.Observe that the intersection point of th curve and is .Given that the vertical line divides into two regions where the area of the region to the left of the line is the area of the region to the right of the line. Therefore the integral expression whose solution gives the value of is calculated as follows.Hence the integral expression whose solution gives the value of is written as follows..