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10 cards from this deck
Differentiation and integration
Differential form and integral form
A(x)=∫axf(t) dtA(x) = \int_a^x f(t) \, dtA(x)=∫axf(t)dt
A(a)=0A(a) = 0A(a)=0 (integral from aaa to aaa has zero width)
Areas below xxx-axis negative, above positive
ddx∫axf(t) dt=f(x)\frac{d}{dx} \int_a^x f(t) \, dt = f(x)dxd∫axf(t)dt=f(x)
∫abf(x) dx=F(b)−F(a)\int_a^b f(x) \, dx = F(b) - F(a)∫abf(x)dx=F(b)−F(a)
Sandwiching technique using rectangles
Only by a constant
f(x)f(x)f(x) must be continuous
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