Solve ∫ (from 5 to 9) of (x^2-4789x^4) wrt x

$$\int _ { 5 } ^ { 9 } ( x ^ { 2 } - 4789 x ^ { 4 } ) d x$$

Evaluate

$$-\frac{803457088}{15}\approx -53563805.866666667$$

Solution Steps

Evaluate the indefinite integral first.

$$\int x^{2}-4789x^{4}\mathrm{d}x$$

Integrate the sum term by term.

$$\int x^{2}\mathrm{d}x+\int -4789x^{4}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x^{2}\mathrm{d}x-4789\int x^{4}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{x^{3}}{3}-4789\int x^{4}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}. Multiply -4789 times \frac{x^{5}}{5}.

$$\frac{x^{3}}{3}-\frac{4789x^{5}}{5}$$

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.

$$\frac{9^{3}}{3}-\frac{4789}{5}\times 9^{5}-\left(\frac{5^{3}}{3}-\frac{4789}{5}\times 5^{5}\right)$$

Simplify.

$$-\frac{803457088}{15}$$