Question
Mathematics Question on Area under Simple Curves
Area of the Region bounded by the curve y=√49-x2 and x-axis is .
A
(A) 49 π sq. units
B
(B) 49 π/2 sq. units
C
(C) 49 π/4 sq. units
D
(D) 98 π sq. units
Answer
(B) 49 π/2 sq. units
Explanation
Solution
The given curve is y = √(49 - x^2).
This is the upper half of a circle with center at the origin and radius 7.
The area bounded by this curve and the x-axis is the area of the upper half of the circle.
The area of a circle with radius r is given by πr^2.
Therefore, the area of the upper half of the circle with radius 7 is: (1/2)π(7^2) = 49π/2 square units.
Hence, the correct option is (B) 49π/2 sq. units.