Solve ∫ (from 3 to 5) of sqrt{245*583}

$$\int _ { 3 } ^ { 5 } \sqrt { 245 \times 583 }$$

Evaluate

$$14\sqrt{2915}\approx 755.870359255$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \sqrt{245\times 583}\mathrm{d}x$$

Find the integral of \sqrt{245\times 583} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{245\times 583}x$$

Simplify.

$$7\sqrt{2915}x$$

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.

$$7\times 2915^{\frac{1}{2}}\times 5-7\times 2915^{\frac{1}{2}}\times 3$$

Simplify.

$$14\sqrt{2915}$$