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Question

The area x-axis, bounded by the curve y = 2kx and x = 0 and x = 2 is 3 log2e, then 22k - 3k = ______________.

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Solution

Given: area of the region bounded by the curve y = 2kx and x = 0 and x = 2 is 3 log2e

We know,
the required area of the region = 02ydx
Thus,
3 log2e=022kxdx±3 log2e=2kxklog202±3log2=1klog22kx02±3k=2kx02±3k=22k-203k=22k-1 or -3k=22k-11=22k-3k or 1=22k+3k22k-3k=1Thus, 22k-3k=1


Hence, 22k − 3k = 1.

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