The area of the region bounded by the curve y = sqrt(16 - x^2) and x-axis is ______.

Question

KollegeApply · Accepted Answer

The area of the region bounded by the curve y = sqrt(16 - x^2) and x-axis is 8 sq.units. Explanation: Here, equation of curve is y = sqrt(16 - x^2) Required area = `2[int_0^4 sqrt(16 - x^2) "d"x] = 2[x/2 sqrt(16 - x^2) + $\frac{16}{2}$ sin^-1 x/4]_0^4 = 2[(0 + 8 sin^-1 $\frac{4}{4}$) - (0 + 0)] = 2[8sin^-1 (1)] = 16 * pi/2` = 8 sq.units. [Solution diagram: 251718_solution_1.png]

AChoose Your Answer