Solve ∫ (from 2 to 3) of 56x-x wrt x

$$\int_{ 2 }^{ 3 } 56x-x d x$$

Evaluate

$$\frac{275}{2}=137.5$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 56x-x\mathrm{d}x$$

Integrate the sum term by term.

$$\int 56x\mathrm{d}x+\int -x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$56\int x\mathrm{d}x-\int x\mathrm{d}x$$

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 56 times \frac{x^{2}}{2}.

$$28x^{2}-\int x\mathrm{d}x$$

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}.

$$28x^{2}-\frac{x^{2}}{2}$$

Simplify.

$$\frac{55x^{2}}{2}$$

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.

$$\frac{55}{2}\times 3^{2}-\frac{55}{2}\times 2^{2}$$

Simplify.

$$\frac{275}{2}$$