What is the integral from 4 to 8 of (x^2)/2-8x+30 ?

The integral from 4 to 8 of (x^2)/2-8x+30 is 8/3

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integral from 4 to 8 of (x^2)/2-8x+30

\int_{4}^{8} \frac{x ^{2}}{2} - 8 x + 30 d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{4}^{8} \frac{x ^{2}}{2} - 8 x + 30 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_{4}^{8} \frac{x ^{2}}{2} d x - \int_{4}^{8} 8 x d x + \int_{4}^{8} 30 d x

\int_{4}^{8} \frac{x ^{2}}{2} d x = \frac{224}{3}

\int_{4}^{8} 8 x d x = 192

\int_{4}^{8} 30 d x = 120

= \frac{224}{3} - 192 + 120

Simplify

\frac{224}{3} - 192 + 120 : \frac{8}{3}

= \frac{8}{3}

\int_{0}^{3} x^{2} + 3 x d x

\int_{- 1}^{4} \frac{4}{3 x ^{2}} d x

\int_{0}^{8} ∣ x - 6 ∣ d x

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

\int_{0}^{1} x^{2} 4 + x^{3} d x

What is the integral from 4 to 8 of (x^2)/2-8x+30 ?
The integral from 4 to 8 of (x^2)/2-8x+30 is 8/3