If the area above the x-axis bounded by the curves $y = {2^{kx}}{\rm{\;and\;}}x = 0\;\,{\rm{and\;}}\,2\;is\,\frac{3}{{\log 2\;}}\;{\rm{then\;the\;value\;of\;}}k{\rm{\;is}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If the area above the x-axis bounded by the curves

y = {2^{kx}}\mathrm{\;and\;}x = 0\;\,\mathrm{and\;}\,2\;is\,\frac{3}{{\log 2\;}}\;\mathrm{then\;the\;value\;of\;}k\mathrm{\;is}

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Correct option: B

Option B, 1, is the correct value of k because when k = 1, the area under the curve y = 2^(kx) from x = 0 to x = 2 equals 3/log(2).

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