Solve ∫ (from 0 to 105) of 1/2x^0 wrt x

$$\int _ { 0 } ^ { 105 } \frac { 1 } { 2 } x ^ { 0 } d x$$

Evaluate

$$\frac{105}{2}=52.5$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$x$$

Simplify.

$$\frac{x}{2}$$

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.

$$\frac{1}{2}\times 105-\frac{1}{2}\times 0$$

Simplify.

$$\frac{105}{2}$$