What is the integral from 1 to 4 of 2x^2+3x-1 ?

The integral from 1 to 4 of 2x^2+3x-1 is 123/2

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integral from 1 to 4 of 2x^2+3x-1

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

\frac{123}{2}

Decimal

61.5

Solution steps

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

\int_{1}^{4} 2 x^{2} d x = 42

\int_{1}^{4} 3 x d x = \frac{45}{2}

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

= 42 + \frac{45}{2} - 3

Simplify

42 + \frac{45}{2} - 3 : \frac{123}{2}

= \frac{123}{2}

What is the integral from 1 to 4 of 2x^2+3x-1 ?
The integral from 1 to 4 of 2x^2+3x-1 is 123/2