حل ∫ (from 1 to 2) of 2x

$$\int _ { 1 } ^ { 2 } 2 x$$

تقدير القيمة

$$3$$

خطوات الحل

Evaluate the indefinite integral first.

$$\int 2x\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2\int x\mathrm{d}x$$

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

$$x^{2}$$

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.

$$2^{2}-1^{2}$$

تبسيط.

$$3$$