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Question

If the area bounded by the curve y=2kx, k>0 and x=0, x=2 and x axis is 3ln2, then the value of k is

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Solution


The given curve is y=2kx, k>0
Clearly, y>0 for all values of x and k
the curve y=22k lies above xaxis for 0x2.
Area bounded by the curve y=2kx,x=0,x=2 is given by:
A=20y dx=202kx dx
=1k2k02t dt, where t=kx
=1k[2tln2]2k0=1kln2(22k1)
Now, A=3ln2(given)
1kln2(22k1)=3ln222k1=3k
k=1

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