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

The integral from 1 to 4 of (sqrt(x)-4x) is -76/3

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integral from 1 to 4 of (sqrt(x)-4x)

\int_{1}^{4} (x - 4 x) d x

- \frac{76}{3}

Decimal

- 25.33333 \dots

Solution steps

\int_{1}^{4} x - 4 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} x d x - \int_{1}^{4} 4 x d x

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

\int_{1}^{4} 4 x d x = 30

= \frac{14}{3} - 30

Simplify

\frac{14}{3} - 30 : - \frac{76}{3}

= - \frac{76}{3}

What is the integral from 1 to 4 of (sqrt(x)-4x) ?
The integral from 1 to 4 of (sqrt(x)-4x) is -76/3