Question

Compute the area of a leaf given by the equation y^2 = (x^2−1)^2 for −1 ≤ x ≤ 1

Answer 1

Using fundamental theorem of calculus, i got the answer -4/3 but on the answer key it isn't.

Answer 2

I get for the area

∫[-1,1] (1-x^2)-(x^2-1) dx = ∫[-1,1] 2-2x^2 dx = 2(x - x^3/3)[-1,1] = 8/3

Answer 3

can you explain it please? where did (1-x^2)-(x^2-1) come from?

Answer 4

y^2 = (x^2−1)^2
y = ±(x^2-1)
That is, y = (x^2-1) or y = (1-x^2)

The area between two functions f(x) and g(x) is ∫ f(x)-g(x) dx.

hat is, it is the sum of all the thin strips whose height is the difference between the curves.