What is the integral from 1 to 3 of sqrt(x-1) ?

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

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integral from 1 to 3 of sqrt(x-1)

\int_{1}^{3} x - 1 d x

\frac{4 2}{3}

Decimal Notation

1.88561 \dots

Solution steps

\int_{1}^{3} x - 1 d x

Apply u-substitution

: \int_{0}^{2} u d u

= \int_{0}^{2} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2}

= [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2}

Compute the boundaries:

\frac{4 2}{3}

= \frac{4 2}{3}

\frac{d y}{d x} = \frac{e ^{x - y}}{1 + e ^{x}}

\int (1 + 4 x)^{- \frac{1}{2}} d x

\int \frac{x ^{2} + 1}{( x - 7 ) ( x - 6 ) ^{2}} d x

\int_{1}^{2} \frac{3}{e ^{4 t}} d t

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