What is the integral from-1 to 3 of (2x^2-x+5) ?

The integral from-1 to 3 of (2x^2-x+5) is 104/3

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integral from-1 to 3 of (2x^2-x+5)

\int_{- 1}^{3} (2 x^{2} - x + 5) d x

\frac{104}{3}

Decimal

34.66666 \dots

Solution steps

\int_{- 1}^{3} 2 x^{2} - x + 5 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}^{3} 2 x^{2} d x - \int_{- 1}^{3} x d x + \int_{- 1}^{3} 5 d x

\int_{- 1}^{3} 2 x^{2} d x = \frac{56}{3}

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

\int_{- 1}^{3} 5 d x = 20

= \frac{56}{3} - 4 + 20

Simplify

\frac{56}{3} - 4 + 20 : \frac{104}{3}

= \frac{104}{3}

t an g e n t y = 3 x + 1, (8, 5)

\int 2 x^{2} - 6 x d x

\frac{d}{d x} (ln ((2 x + 3)^{4}) (x + 1)^{3})

d er i v a t i v e y = - 2 e^{5 x^{2}}

4 y^{^{''}} - 25 y = 0

What is the integral from-1 to 3 of (2x^2-x+5) ?
The integral from-1 to 3 of (2x^2-x+5) is 104/3