Solve ∫ (from 1 to 2) of 2n-1

$$\int _ { 1 } ^ { 2 } 2 n - 1$$

Evaluate

$$2n-1$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2n-1\mathrm{d}x$$

Find the integral of 2n-1 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(2n-1\right)x$$

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.

$$\left(2n-1\right)\times 2-\left(2n-1\right)$$

Simplify.

$$2n-1$$

Differentiate w.r.t. n

$$2$$