If the area above the x-axis, bounded by the curves y = 2^kx and x = 0, and x = 2 is then the value of k is

Question

If the area above the x-axis, bounded by the curves y = 2 kx and x = 0, and x = 2 is then the value of k is

Philoid · Accepted Answer

The area can be computed as –

Comparing with

⇒ 4^k = 3^k + 1

Using Binomial Theorem,

This equality holds only when k = 1, because only then you get two terms in the expansion.

Ans: k = 1

If the area above the x-axis, bounded by the curves y = 2kx and x = 0, and x = 2 is then the value of k is