Solve ∫ (from 3 to 6) of (3-0,5X)(3-0,5X) wrt x

$$\int _ { 3 } ^ { 6 } ( 3 - 0,5 X ) ( 3 - 0,5 X ) d x$$

Evaluate

$$3\left(-\frac{X}{2}+3\right)^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \left(3-\frac{X}{2}\right)\left(3-\frac{X}{2}\right)\mathrm{d}x$$

Find the integral of \left(3-\frac{X}{2}\right)\left(3-\frac{X}{2}\right) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(3-\frac{X}{2}\right)\left(3-\frac{X}{2}\right)x$$

Simplify.

$$\left(3-\frac{X}{2}\right)^{2}x$$

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.

$$\left(3-0,5X\right)^{2}\times 6-\left(3-0,5X\right)^{2}\times 3$$

Simplify.

$$3\left(3-\frac{X}{2}\right)^{2}$$

Differentiate w.r.t. X

$$\frac{3X}{2}-9$$