MH Board · Chapter

Application of Definite Integration

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is

\int_a^b |y|\,dx

;

a part below the axis gives a negative integral, so take its size

Start

Area between a curve and the Y-axisBetween

x = g(y)

, the Y-axis and

y = c

,

y = d

, the area is

\int_c^d |x|\,dy

: integrate along

y

with horizontal stripsLocked

Areas of circles, ellipses and parabolasUse symmetry: find one quarter and multiply; the ellipse

\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1

encloses

\pi ab

, using

\int_0^a \sqrt{a^2 - x^2}\,dx = \dfrac{\pi a^2}{4}

Locked

Area between two curvesFind where the curves meet, then integrate (upper

-

lower)

dx

between those points, or (right

-

left)

dy

Locked