Question
areas between the curves
x=y^2-2, x=y, y=3.
int[a,b](f(y)-g(y)) dy
i know how to graph. but im have problem with integral.
x=y^2-2, x=y, y=3.
int[a,b](f(y)-g(y)) dy
i know how to graph. but im have problem with integral.
Answers
Steve
y^2-2 intersects y at (2,2)
y=3 intersects x=y at (3,3)
y^2-2 intersects y=3 at (7,3)
the are a can be gotten by integration either along x or y. Along y,
a = ∫[2,3](y^2-2)-y dy = 11/6
a = ∫[2,3]x - √(x+2) dx + ∫[3,7]3 - √(x+2) dx
= 1/6 (47-20√5) + 1/3 (10√5-6) = 11/6
y=3 intersects x=y at (3,3)
y^2-2 intersects y=3 at (7,3)
the are a can be gotten by integration either along x or y. Along y,
a = ∫[2,3](y^2-2)-y dy = 11/6
a = ∫[2,3]x - √(x+2) dx + ∫[3,7]3 - √(x+2) dx
= 1/6 (47-20√5) + 1/3 (10√5-6) = 11/6