Definite integration:

If f(x) > 0 for all x Î [a, b]; then是数值方程l to area bounded by curve y = f(x), then x axis and the straight lines x = a and x = b that is

Generallyrepresents to algebraic sum of the figures bounded by curve

y = f(x), x axis and the straight line x = a and x = b. The areas above x axis are taken place plus sign and the areas below x-axis are taken with minus sign that is,

area OLA - area AQM - area MRB + area BSCD

Note:dx =, represents algebraic sum of areas means, that if the area of function y = f(x) is asked between a to b.

=>Area bounded =dx and not been represented bydx

For example, if someone asks the area of y = x³between -1 to 1.

Then y = x³could be plotted as;

or, by using above definition Area

But if, we integrate x³between -1 to 1.

which does not represent the area.

Therefore, students are adviced to make difference between area and definite Integral.

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