Solve ∫ (from 1 to 11) of sqrt{(39/10-15/10)^2}

$$\int _ { 1 } ^ { 11 } \sqrt { ( \frac { 39 } { 10 } - \frac { 15 } { 10 } ) ^ { 2 } }$$

Evaluate

$$24$$

Solution Steps

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\int _{1}^{11}\sqrt{\left(\frac{39}{10}-\frac{3}{2}\right)^{2}}\mathrm{d}x$$

Subtract \frac{3}{2} from \frac{39}{10} to get \frac{12}{5}.

$$\int _{1}^{11}\sqrt{\left(\frac{12}{5}\right)^{2}}\mathrm{d}x$$

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\int _{1}^{11}\sqrt{\frac{144}{25}}\mathrm{d}x$$

Rewrite the square root of the division \frac{144}{25} as the division of square roots \frac{\sqrt{144}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\int _{1}^{11}\frac{12}{5}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{12}{5}\mathrm{d}x$$

Find the integral of \frac{12}{5} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{12x}{5}$$

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.

$$\frac{12}{5}\times 11-\frac{12}{5}$$

Simplify.

$$24$$