What is the integral from 0 to 4 of 8+7sqrt(x) ?

The integral from 0 to 4 of 8+7sqrt(x) is 208/3

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integral from 0 to 4 of 8+7sqrt(x)

\int_{0}^{4} 8 + 7 x d x

\frac{208}{3}

Decimal

69.33333 \dots

Solution steps

\int_{0}^{4} 8 + 7 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{4} 8 d x + \int_{0}^{4} 7 x d x

\int_{0}^{4} 8 d x = 32

\int_{0}^{4} 7 x d x = \frac{112}{3}

= 32 + \frac{112}{3}

Simplify

32 + \frac{112}{3} : \frac{208}{3}

= \frac{208}{3}

\int_{- 3}^{0} g (t) d t

\int_{0}^{0.4} x^{2} d x

\int_{0}^{1} 7 x^{3} d x

\int_{0}^{1} 9 x (x^{2} - 1)^{7} d x

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

What is the integral from 0 to 4 of 8+7sqrt(x) ?
The integral from 0 to 4 of 8+7sqrt(x) is 208/3