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3.3.2. The geometric meaning of a definite integral

Lecture



Let the function y = f ( x ) ≥ 0 be continuous (and therefore integrable) on the segment [ a, b ] (Fig. 13). The integral sum S n with f ( x ) ≥ 0 is equal to the area of ​​the figure composed of rectangles with sides f (ξ i ) · h i . Consequently, the limit of the sequence S n as h → 0 is equal to the area S of the curvilinear trapezium, i.e. figures bounded by the line y = f ( x ) , axis OX and straight lines x = a, x = b :   3.3.2.  The geometric meaning of a definite integral

  3.3.2.  The geometric meaning of a definite integral

Fig. 13


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Mathematical analysis. Integral calculus

Terms: Mathematical analysis. Integral calculus