What is the integral from 0 to 4 of sqrt(1+x) ?

The integral from 0 to 4 of sqrt(1+x) is (10sqrt(5)-2)/3

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integral from 0 to 4 of sqrt(1+x)

\int_{0}^{4} 1 + x d x

\frac{10 5 - 2}{3}

Decimal Notation

6.78689 \dots

Solution steps

\int_{0}^{4} 1 + x d x

Apply u-substitution

: \int_{1}^{5} u d u

= \int_{1}^{5} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

Compute the boundaries:

\frac{10 5}{3} - \frac{2}{3}

= \frac{10 5}{3} - \frac{2}{3}

Simplify

= \frac{10 5 - 2}{3}

\int \frac{- 1}{1 - x} d x

\int_{1}^{3} (- x^{2} + 4 x - 3) d x

x \to (0) lim (\frac{ln ( x )}{x})

x \to - 3 lim (2 x - 3 a x + 6 a)

x \to 1 + lim (\frac{∣ x - 1 ∣}{x - 1})

What is the integral from 0 to 4 of sqrt(1+x) ?
The integral from 0 to 4 of sqrt(1+x) is (10sqrt(5)-2)/3