Solve ∫ (from 1 to 2) of x^2/2/x wrt x

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

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Express \frac{\frac{x^{2}}{2}}{x} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Evaluate the indefinite integral first.

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

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

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

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}.

$$\frac{x^{2}}{4}$$

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.

$$\frac{2^{2}}{4}-\frac{1^{2}}{4}$$

Simplify.

$$\frac{3}{4}$$