What is the integral from 2 to 4 of x^2+5x+7+1 ?

The integral from 2 to 4 of x^2+5x+7+1 is 194/3

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integral from 2 to 4 of x^2+5x+7+1

\int_{2}^{4} x^{2} + 5 x + 7 + 1 d x

\frac{194}{3}

Decimal

64.66666 \dots

Solution steps

\int_{2}^{4} x^{2} + 5 x + 7 + 1 d x

Simplify

= \int_{2}^{4} x^{2} + 5 x + 8 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_{2}^{4} x^{2} d x + \int_{2}^{4} 5 x d x + \int_{2}^{4} 8 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 5 x d x = 30

\int_{2}^{4} 8 d x = 16

= \frac{56}{3} + 30 + 16

Simplify

\frac{56}{3} + 30 + 16 : \frac{194}{3}

= \frac{194}{3}

What is the integral from 2 to 4 of x^2+5x+7+1 ?
The integral from 2 to 4 of x^2+5x+7+1 is 194/3