AREA

thnx ur ri8..i also got the same answer but the doubt is

we know f(x) = √(1-x² gives a circle of area pi

let -1 to +1 ∫f(x)dx = pi

we know \int_{ca}^{cb}{}f(t)dt = c\int_{a}^{b}{}f(ct)dt

b{f(x/a)} gives the ellipse

using above property b\int_{-a}^{a}{}f(x/a) = ab\int_{-1}^{1}{}f(x)

which gives area of ellipse equal to pi ab

but -1 to +1 ∫f(x)dx ≠pi

but still we are getting the area correct,why?

if u r taking f = √1-x² , then that is the curve only above the x axis , so you are calculating only half of the area when u r writing -1 to +1 ∫f(x)dx

same for ellipse, u r calculating only half of ellipse's area