What is the integral from 1 to 4 of 7x+sqrt(x) ?

The integral from 1 to 4 of 7x+sqrt(x) is 343/6

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integral from 1 to 4 of 7x+sqrt(x)

\int_{1}^{4} 7 x + x d x

\frac{343}{6}

Decimal

57.16666 \dots

Solution steps

\int_{1}^{4} 7 x + 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_{1}^{4} 7 x d x + \int_{1}^{4} x d x

\int_{1}^{4} 7 x d x = \frac{105}{2}

\int_{1}^{4} x d x = \frac{14}{3}

= \frac{105}{2} + \frac{14}{3}

Simplify

\frac{105}{2} + \frac{14}{3} : \frac{343}{6}

= \frac{343}{6}

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What is the integral from 1 to 4 of 7x+sqrt(x) ?
The integral from 1 to 4 of 7x+sqrt(x) is 343/6