The area bounded by the curve y = 4x – x^2 and the x-axis is A. 30/7 sq. units

Question

The area bounded by the curve y = 4x – x² and the x-axis is

A. \(\frac{30}{7}\) sq. units

B. \(\frac{31}{7}\) sq. units

C. \(\frac{32}{3}\) sq. units

D. \(\frac{34}{3}\) sq. units

Answer 1

Correct answer is C.

y = 4x – x

This is a parabola with negative co-efficient of x², i.e., it’s a downward parabola.

So, area A enclosed is the area of the peak of the parabola above the x – axis.

We need to find the bounds of this peak.

Now, at the point where the peak starts/ends, y = 0,

i.e., 4x – x² = 0

⇒ x(4 – x) = 0

⇒ x = 0 or x = 4