Q1 of 123 Page 22

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

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

Find the area bounded by the parabola y² = 4x and the line y = 2x – 4.

(i) By using horizontal strips

(ii) By using vertical strips.

Find the area of the region bounded by the parabola y² = 2x and the straight-line x – y = 4.

The area included between the parabolas y² = 4x and x² = 4y is (in square units)

The area bounded by the curve y = log_e x and x-axis and the straight line x = e is

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