What is the integral from 0 to x of sqrt(t+3) ?

The integral from 0 to x of sqrt(t+3) is (2(x+3)^{3/2})/3-2sqrt(3)

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integral from 0 to x of sqrt(t+3)

\int_{0}^{x} t + 3 d t

\frac{2 ( x + 3 ) ^{\frac{3}{2}}}{3} - 23

Solution steps

\int_{0}^{x} t + 3 d t

Apply u-substitution

: \int_{3}^{x + 3} u d u

= \int_{3}^{x + 3} u d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{2}{3} (x + 3)^{\frac{3}{2}} - 23

= \frac{2}{3} (x + 3)^{\frac{3}{2}} - 23

Simplify

= \frac{2 ( x + 3 ) ^{\frac{3}{2}}}{3} - 23

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What is the integral from 0 to x of sqrt(t+3) ?
The integral from 0 to x of sqrt(t+3) is (2(x+3)^{3/2})/3-2sqrt(3)