Solve ∫ (from 0 to 4) of -1-11.75x wrt x

$$\int_{ 0 }^{ 4 } -1-11.75x d x$$

Evaluate

$$-98$$

Solution Steps

Evaluate the indefinite integral first.

$$\int -1-\frac{47x}{4}\mathrm{d}x$$

Integrate the sum term by term.

$$\int -1\mathrm{d}x+\int -\frac{47x}{4}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int -1\mathrm{d}x-\frac{47\int x\mathrm{d}x}{4}$$

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

$$-x-\frac{47\int x\mathrm{d}x}{4}$$

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 -11.75 times \frac{x^{2}}{2}.

$$-x-\frac{47x^{2}}{8}$$

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.

$$-4-\frac{47}{8}\times 4^{2}-\left(-0-\frac{47}{8}\times 0^{2}\right)$$

Simplify.

$$-98$$