Question

Determine the area under the curve y = √(a2 – x2), included between the lines x = 0 and x = 4.

Answer 1

The equation of the curve is y = √(a2 – x2)

We can write it as y2 = a2 – x2

y2 + x2 = a2 ….. (1)

Here we know that x2 + y2 = a2 represents a circle having center at O (0, 0) and a units as the radius

Similarly x2 + y2 = a2 has even power of x and y and is symmetrical about x and y-axis.

So the required area = area of OAB