Solve \(\int_{3}^{4} \sqrt{x} d x\)

Evaluate

\int_{3}^{4} x d x

Evaluate the integral

\int x d x

Use the property of integral \int x^{n} d x = \frac{x ^{n + 1}}{n + 1}

\frac{x ^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}

Add the numbers

More Steps

\frac{x ^{\frac{3}{2}}}{\frac{1}{2} + 1}

Add the numbers

More Steps

\frac{x ^{\frac{3}{2}}}{\frac{3}{2}}

Multiply by the reciprocal

x^{\frac{3}{2}} \times \frac{2}{3}

Use the commutative property to reorder the terms

\frac{2}{3} x^{\frac{3}{2}}

Return the limits

(\frac{2}{3} x^{\frac{3}{2}})_{3}^{4}

Calculate the value

More Steps

\frac{16}{3} - 2 \times 3^{\frac{1}{2}}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

\frac{16}{3} - 23

Solution

\frac{16 - 6 3}{3}

Alternative Form

\approx 1.869232