Solve ∫ _{1/5}^frac{1{4}}1.2-x wrt x

$$\int_{ \frac{ 1 }{ 5 } }^{ \frac{ 1 }{ 4 } } 1.2-x d x$$

Evaluate

$$0.04875$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 1.2-x\mathrm{d}x$$

Integrate the sum term by term.

$$\int 1.2\mathrm{d}x+\int -x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 1.2\mathrm{d}x-\int x\mathrm{d}x$$

Find the integral of 1.2 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{6x}{5}-\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply -1 times \frac{x^{2}}{2}.

$$\frac{6x}{5}-\frac{x^{2}}{2}$$

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.

$$1.2\times \frac{1}{4}-\frac{\left(\frac{1}{4}\right)^{2}}{2}-\left(1.2\times \frac{1}{5}-\frac{\left(\frac{1}{5}\right)^{2}}{2}\right)$$

Simplify.

$$\frac{39}{800}$$