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10 cards from this deck
It approximates the area under a curve or integral.
Width hhh, function values f(x0)f(x_0)f(x0), f(x1)f(x_1)f(x1), ..., f(xn)f(x_n)f(xn).
h=(b−a)/nh = (b - a) / nh=(b−a)/n, where [a,b][a, b][a,b] is the interval.
Divide the interval [a,b][a, b][a,b] into nnn equal parts.
Evaluate f(x)f(x)f(x) at each division point x0,...,xnx_0,...,x_nx0,...,xn.
Area ≈h2[f(x0)+2f(x1)+...+f(xn)]\approx \frac{h}{2} [f(x_0) + 2f(x_1) + ... + f(x_n)]≈2h[f(x0)+2f(x1)+...+f(xn)]
The area was found using numerical approximation methods.
Two intervals were used in Example 2.
The trapezoidal rule is used in Example 2.
It approximates continuous functions over an interval.
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