Solve ∫ (from 2 to 4) of (-x^2+6x-8) wrt x=1/k

$$\int _ { 2 } ^ { 4 } ( - x ^ { 2 } + 6 x - 8 ) d x = \frac { 1 } { k }$$

Solve for k

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

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by k.

$$k\int _{2}^{4}-x^{2}+6x-8\mathrm{d}x=1$$

The equation is in standard form.

$$\frac{4}{3}k=1$$

Divide both sides of the equation by \frac{4}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{3}k}{\frac{4}{3}}=\frac{1}{\frac{4}{3}}$$

Dividing by \frac{4}{3} undoes the multiplication by \frac{4}{3}.

$$k=\frac{1}{\frac{4}{3}}$$

Divide 1 by \frac{4}{3} by multiplying 1 by the reciprocal of \frac{4}{3}.

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