If m ≤ f(x) ≤ m for a ≤ x ≤ b, where m is the absolute minimum and m is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a ≤ m(b − a). use this property to estimate the value of the integral. 2 4 1 x2 dx 0 (smaller value) (larger value)

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation: