What is the integral from 0 to 4 of 2pixsqrt(x) ?

The integral from 0 to 4 of 2pixsqrt(x) is (128pi)/5

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integral from 0 to 4 of 2pixsqrt(x)

\int_{0}^{4} 2 π x x d x

\frac{128 π}{5}

Decimal Notation

80.42477 \dots

Solution steps

\int_{0}^{4} 2 π x x d x

Take the constant out:

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

= 2 π \cdot \int_{0}^{4} x x d x

Simplify

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

= 2 π \cdot \int_{0}^{4} x^{\frac{3}{2}} d x

Apply the Power Rule

: [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{4}

= 2 π [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{4}

Compute the boundaries:

\frac{64}{5}

= 2 π \frac{64}{5}

Simplify

= \frac{128 π}{5}

\frac{d}{d x} (\frac{1}{1 + e ^{\frac{1}{x}}})

\int \frac{50}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

\frac{d}{d x} (\frac{d y}{d x}) + k^{2} y = a e^{- b x}

\frac{2}{s + 8}

(- 4, 2), (- 1, - 5)

What is the integral from 0 to 4 of 2pixsqrt(x) ?
The integral from 0 to 4 of 2pixsqrt(x) is (128pi)/5