According to the lecture, Simpson's rule integrates exactly any functions that are constants, linear, or parabolas.
Conditions: The method fits three points to a parabola and integrates that parabola.; Applies to constant, linear, and quadratic functions as stated in the lecture.
According to the lecture, Simpson's rule integrates exactly any functions that are constants, linear, or parabolas.
Conditions: The method fits three points to a parabola and integrates that parabola.; Applies to constant, linear, and quadratic functions as stated in the lecture.
Simpson's rule approximates the integral by fitting three points of the function to a parabola and then integrating that parabola. It is exact for constant, linear, and quadratic functions.
Conditions: Uses three points of the function on the integration interval.; Exact for constant, linear, and quadratic functions according to the lecture statement.
Simpson's rule approximates the integral by fitting three points of the function to a parabola and then integrating that parabola. It is exact for constant, linear, and quadratic functions.
Conditions: Uses three points of the function on the integration interval.; Exact for constant, linear, and quadratic functions according to the lecture statement.
The trapezoidal rule approximates an integral by replacing the curve over an interval with a straight line between two sampled points and computing the area of the resulting trapezoid. In composite form, the endpoint values are each weighted by one half because interior points belong to two neighboring trapezoids, while endpoints belong to only one.
Conditions: Applied to numerical integration over an interval [a,b].; Uses function values at the interval endpoints.; For composite use, adjacent subinterval endpoints are shared, producing half weights at the outer endpoints.
The trapezoidal rule approximates an integral by replacing the curve over an interval with a straight line between two sampled points and computing the area of the resulting trapezoid. In composite form, the endpoint values are each weighted by one half because interior points belong to two neighboring trapezoids, while endpoints belong to only one.
Conditions: Applied to numerical integration over an interval [a,b].; Uses function values at the interval endpoints.; For composite use, adjacent subinterval endpoints are shared, producing half weights at the outer endpoints.