Question
Mathematics Question on Straight lines
What is the area of the region bounded by the curve f(x)=1−x24,x∈[−2,2] and the x-axis?
A
(A) 83 square units
B
(B) 43 square units
C
(C) 23 square units
D
(D) 13 square units
Answer
(A) 83 square units
Explanation
Solution
Explanation:
We know that: The area of the region bounded by the curve f(x),x∈[−a,a] and the x-axis is given by:A=∫−aaf(x)dxTherefore,The area of the region bounded by the curve f(x)=1−x24,x∈[−2,2] and the x-axis will be:A=∫−22(1−x24)dx⇒A=[x−x312]−22⇒A=[2−(−2)]−[812−−812]⇒A=4−43⇒A=83Therefore, the area of the region bounded by the curve f(x)=1−x24,x∈[−2,2] and the x-axis is 83 square units.Hence, the correct option is (A).