The area enclosed by the curve y2 + x4 = x2 is-(a)2/3(b)4/3(c)8/3(d)10/3
The area enclosed by the curve y2 + x4 = x2 is-
(a)2/3
(b)4/3
(c)8/3
(d)10/3
Snehal Jadhav , 6 Years ago
Grade 12
Integral Calculus> The area enclosed by the curve y 2 + x 4 ...
1 Answers
Arun
Last Activity: 6 Years ago
Dear student
This curve is symmetrical along the x and y axis, so we can integrate the area in the first quadrant and multiply it by 4.
y = x(√(1-x^2))
A = ∫ 0->1 x(√(1-x^2)) dx
A = -1/3 (1-x^2)^(3/2) | 0->1
A = 1/3
Total Area is 1/3 x 4 = 4/3
y = x(√(1-x^2))
A = ∫ 0->1 x(√(1-x^2)) dx
A = -1/3 (1-x^2)^(3/2) | 0->1
A = 1/3
Total Area is 1/3 x 4 = 4/3
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