Question

integral of sqrt(9-y^2)*dy from -3 to 3

What does this represents?

Answer 1

i think it is the right half of a circle, is it correct?

Answer 2

notice that you're finding the area of a semicircle... from -3 to 3

Answer 3

yes...

Answer 4

x = sqrt(9-y^2)
x^2 + y^2 = 9
So that integral represents the area of the right semicircle

Answer 5

would the area be 0, since above x and below x values would cancel each other

Answer 6

no... you're integrating wrt y....

Answer 7

what's the difference with something wrt x

Answer 8

When you integrate wrt x-axis, you're finding the area that's bounded by the curve and the x-axis, which the 2 quadrants will cancel each other out. However, since it's "dy", you're finding area bounded by the curve and y-axis, which looks at left and right.