What is the integral from 2 to 6 of 3pi(sqrt(x^5)) ?

The integral from 2 to 6 of 3pi(sqrt(x^5)) is (3pi(432sqrt(6)-16sqrt(2)))/7

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integral from 2 to 6 of 3pi(sqrt(x^5))

\int_{2}^{6} 3 π (x^{5}) d x

\frac{3 π ( 432 6 - 16 2 )}{7}

Decimal

1394.26415 \dots

Solution steps

\int_{2}^{6} 3 π x^{5} d x

Take the constant out:

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

= 3 π \cdot \int_{2}^{6} x^{5} d x

x^{5} = x^{\frac{5}{2}},

assuming

x \geq 0

= 3 π \cdot \int_{2}^{6} x^{\frac{5}{2}} d x

Apply the Power Rule

= 3 π [\frac{2}{7} x^{\frac{7}{2}}]_{2}^{6}

Compute the boundaries:

\frac{432 6 - 16 2}{7}

= 3 π \frac{432 6 - 16 2}{7}

Simplify

= \frac{3 π ( 432 6 - 16 2 )}{7}

What is the integral from 2 to 6 of 3pi(sqrt(x^5)) ?
The integral from 2 to 6 of 3pi(sqrt(x^5)) is (3pi(432sqrt(6)-16sqrt(2)))/7