حل ∫ (from 1 to 300) of 1/x^2 wrt x

$$\int _ { 1 } ^ { 300 } \frac { 1 } { x ^ { 2 } } d x$$

تقدير القيمة

$$\frac{299}{300}\approx 0.996666667$$

خطوات الحل

Evaluate the indefinite integral first.

$$\int \frac{1}{x^{2}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}.

$$-\frac{1}{x}$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$-300^{-1}+1^{-1}$$

تبسيط.

$$\frac{299}{300}$$