Question

find by integration the area of the circle x2+y2=16

Answer 1

the givn circle has the radius 4unit

so area = πr^2

area = 16π sq.unit

Answer 2

Answer:

the area of the circle$x^2 + y^2 = 16$ is 4π

Step-by-step explanation:

Given, equation of circle is

    $x^2 + y^2 = 16$

$= > x^2 + y^2 = 16$

$= > y^2 = 16 - x^2$

$= > Y =\sqrt{(16 - x^2 )}$

Now, area of the circle is defined as A = 0∫4 √(42 - x2 ) dx

=> A = (1/2) * [x√(42 - x2 ) + 42 * sin-1 (x/4) 0]4  {apply √(a2 - x2 ) formula}

=> A = (1/2) * [16 * sin-1 (4/4)]

=> A = 8 * sin-1 (1)

=> A = 8 * π/2

=> A = 4π

So, the area of the circle x2 + y2 = 16 is 4π