Thus, definite integral is net area: area above x-axis minus area below x-axis Example 1. Express `lim_(n->oo)sum_(i=1)^n[3x_i^2-cos(x_i^5)]Delta x` as an integral on the interval `[0,pi]` . Comparing the given limit with the limit in definition of integral, we see that they will be identical if we choose...
Apr 18, 2016 · If f is defined on the closed interval [a, b] and the limit of a Riemann sum of f exists, then we say f is integrable on [a, b] and we denote the limit by ∫∑ =∆ = →∆ b a n i ii x dxxfxcf )()(lim 1 0 The limit is called the definite integral of f from a to b.