What is the integral from-1 to 8 of 3sqrt(x+1) ?

The integral from-1 to 8 of 3sqrt(x+1) is 54

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integral from-1 to 8 of 3sqrt(x+1)

\int_{- 1}^{8} 3 x + 1 d x

54

Solution steps

\int_{- 1}^{8} 3 x + 1 d x

Take the constant out:

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

= 3 \cdot \int_{- 1}^{8} x + 1 d x

Apply u-substitution

: \int_{0}^{9} u d u

= 3 \cdot \int_{0}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9}

= 3 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9}

Compute the boundaries:

18

= 3 \cdot 18

Simplify

= 54

\int_{0}^{9} (x) d x

\int_{0}^{3} 4^{4 x} d x

\int_{1}^{8} 3 x d x

\int_{\frac{π}{3}}^{π} (sin (x)) d x

\int_{- \frac{π}{3}}^{\frac{π}{3}} cos (x) d x

What is the integral from-1 to 8 of 3sqrt(x+1) ?
The integral from-1 to 8 of 3sqrt(x+1) is 54