Question

If A(n) represents the area bounded by the curve y = n . lnx, where n e N and n > 1, the x-axis and the lines x = 1 and x = e, then the value of A(n) + n A(n − 1) is equal to

• A. $\frac { n ^ { 2 } } { e + 1 }$
• B. $\frac { n ^ { 2 } } { e - 1 }$
• C. n²
• D. e.n²

Answer 1

Answer: (C)

n²

Answer 2

A(n) = = n

⇒ A(n – 1) = (n – 1)

⇒ A(n) + n.A(n - 1) = n + n(n – 1) = n².