\int _ { 1 } ^ { 2 } 2 d x d x
Evaluate
3d
Differentiate w.r.t. d
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\int 2dx\mathrm{d}x
Evaluate the indefinite integral first.
2d\int x\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.
2d\times \frac{x^{2}}{2}
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}.
x^{2}d
Simplify.
2^{2}d-1^{2}d
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.
3d
Simplify.
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