What is the integral from 1 to 4 of 14x^{5/2} ?

The integral from 1 to 4 of 14x^{5/2} is 508

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integral from 1 to 4 of 14x^{5/2}

\int_{1}^{4} 14 x^{\frac{5}{2}} d x

508

Solution steps

\int_{1}^{4} 14 x^{\frac{5}{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 14 \cdot \int_{1}^{4} x^{\frac{5}{2}} d x

Apply the Power Rule

: [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{4}

= 14 [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{4}

Compute the boundaries:

\frac{254}{7}

= 14 \cdot \frac{254}{7}

Simplify

= 508

\int_{- 1}^{1} 5 - 4 x d x

\int_{- 1}^{1} (3 x - 2) d x

\int_{1}^{0} 6 x (2 - x) d x

\int_{1}^{3} (3 x^{2} + 2) d x

\int_{0}^{π} x (sin (x))^{2} d x

What is the integral from 1 to 4 of 14x^{5/2} ?
The integral from 1 to 4 of 14x^{5/2} is 508