Question

Evaluate \[\int\limits_{-1}^{0}\sqrt{1-x ^{2}}dx \] by interpreting it in terms of area

Answer 1

i would draw a triangle

Answer 2

it's the top half a circle with diameter 1

Answer 3

theres your answer =)

Answer 4

actually its r= 1

Answer 5

and x goes from -1 to 0 so its a quater circle

Answer 6

If \( y = \sqrt{1-x^2} \), then
\( y^2 = 1 -x^2 \)
or \( x^2 + y^2 = 1 \)

Hence it is indeed a circle of radius r = 1 and it's the quarter lying in the 2nd quadrant.