What is the integral from 0 to 10 of sqrt(1+x) ?

The integral from 0 to 10 of sqrt(1+x) is (22sqrt(11)-2)/3

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integral from 0 to 10 of sqrt(1+x)

\int_{0}^{10} 1 + x d x

\frac{22 11 - 2}{3}

Decimal

23.65524 \dots

Solution steps

\int_{0}^{10} 1 + x d x

Apply u-substitution

= \int_{1}^{11} u d u

Apply the Power Rule

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{11}

Compute the boundaries:

\frac{22 11}{3} - \frac{2}{3}

= \frac{22 11}{3} - \frac{2}{3}

Simplify

= \frac{22 11 - 2}{3}

\int_{- \infty}^{0} \frac{1}{6 - 5 x} d x

x^{2} \cdot \frac{d y}{d x} = y - x y

\int (x^{2} y) d y

y^{^{''}} + 4 y = x e^{x}

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 14, y^{^{'}} (0) = b

What is the integral from 0 to 10 of sqrt(1+x) ?
The integral from 0 to 10 of sqrt(1+x) is (22sqrt(11)-2)/3