What is the integral from 1 to 4 of (2sqrt(x)) ?

The integral from 1 to 4 of (2sqrt(x)) is 28/3

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integral from 1 to 4 of (2sqrt(x))

\int_{1}^{4} (2 x) d x

\frac{28}{3}

Decimal Notation

9.33333 \dots

Solution steps

\int_{1}^{4} 2 x d x

Take the constant out:

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

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

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

= 2 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{14}{3}

= 2 \cdot \frac{14}{3}

Simplify

= \frac{28}{3}

\int_{0}^{π} cos (\frac{1}{2}) x d x

x \to \frac{π}{2} lim (\frac{cos ( x )}{1 - sin ( x )})

x \to \frac{π}{2} lim (\frac{ln ( sin ( x ) )}{( π - 2 x ) ^{2}})

x \to 3 lim ((2 x - 4)^{4} (x - 2))

x \to 4 lim (\frac{x ^{2} + 4}{5})

What is the integral from 1 to 4 of (2sqrt(x)) ?
The integral from 1 to 4 of (2sqrt(x)) is 28/3