Solve ∫ (from 3 to 4) of k^2+2k-1

$$\int _ { 3 } ^ { 4 } k ^ { 2 } + 2 k - 1$$

Evaluate

$$k^{2}+2k-1$$

Solution Steps

Evaluate the indefinite integral first.

$$\int k^{2}+2k-1\mathrm{d}x$$

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

$$\left(k^{2}+2k-1\right)x$$

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.

$$\left(k^{2}+2k-1\right)\times 4-\left(k^{2}+2k-1\right)\times 3$$

Simplify.

$$-1+2k+k^{2}$$

Differentiate w.r.t. k

$$2\left(k+1\right)$$