What is the integral from 4 to 5 of x^2+2x-11 ?

The integral from 4 to 5 of x^2+2x-11 is 55/3

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integral from 4 to 5 of x^2+2x-11

\int_{4}^{5} x^{2} + 2 x - 11 d x

\frac{55}{3}

Decimal

18.33333 \dots

Solution steps

\int_{4}^{5} x^{2} + 2 x - 11 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}^{5} x^{2} d x + \int_{4}^{5} 2 x d x - \int_{4}^{5} 11 d x

\int_{4}^{5} x^{2} d x = \frac{61}{3}

\int_{4}^{5} 2 x d x = 9

\int_{4}^{5} 11 d x = 11

= \frac{61}{3} + 9 - 11

Simplify

\frac{61}{3} + 9 - 11 : \frac{55}{3}

= \frac{55}{3}

\int_{0}^{4} (x^{2} - 5) d x

\int_{0}^{1} \frac{2 x}{3} d x

\int_{- 2}^{20} ∣ x - 10 ∣ d x

\int_{0}^{3} \frac{1}{( x - 3 ) ^{2}} d x

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

What is the integral from 4 to 5 of x^2+2x-11 ?
The integral from 4 to 5 of x^2+2x-11 is 55/3