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The three rectangle rules differ only in the choice of sample point used to determine the rectangle height on equal-width subintervals. The left rule uses the left endpoint, the right rule uses the right endpoint, and the midpoint rule uses the center of each subinterval.

Conditions: The subintervals have the same width.; The method approximates area under a curve by sums of rectangles.

The three rectangle rules differ only in the choice of sample point used to determine the rectangle height on equal-width subintervals. The left rule uses the left endpoint, the right rule uses the right endpoint, and the midpoint rule uses the center of each subinterval.

Conditions: The subintervals have the same width.; The method approximates area under a curve by sums of rectangles.

Numerical quadrature is the method of calculating integrals using a numerical approach rather than relying on symbolic integration.

Conditions: Applies when an integral is evaluated approximately by computation rather than exactly by analytic antiderivatives.

Numerical quadrature is the method of calculating integrals using a numerical approach rather than relying on symbolic integration.

Conditions: Applies when an integral is evaluated approximately by computation rather than exactly by analytic antiderivatives.