What is the integral from-2 to 0 of 2x^2+5x+6 ?

The integral from-2 to 0 of 2x^2+5x+6 is 22/3

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integral from-2 to 0 of 2x^2+5x+6

\int_{- 2}^{0} 2 x^{2} + 5 x + 6 d x

\frac{22}{3}

Decimal Notation

7.33333 \dots

Solution steps

\int_{- 2}^{0} 2 x^{2} + 5 x + 6 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}^{0} 2 x^{2} d x + \int_{- 2}^{0} 5 x d x + \int_{- 2}^{0} 6 d x

\int_{- 2}^{0} 2 x^{2} d x = \frac{16}{3}

\int_{- 2}^{0} 5 x d x = - 10

\int_{- 2}^{0} 6 d x = 12

= \frac{16}{3} - 10 + 12

Simplify

\frac{16}{3} - 10 + 12 : \frac{22}{3}

= \frac{22}{3}

f (x) = - \frac{3}{2} x^{3} + \frac{2}{5} x^{2} - 4

g (t) = \frac{7}{8 t ^{5}}

\int 3 sin (6 x) d x

\frac{d ^{2}}{d x ^{2}} (- \frac{x}{y})

y^{^{''}} + 36 y = 6 t^{2}

What is the integral from-2 to 0 of 2x^2+5x+6 ?
The integral from-2 to 0 of 2x^2+5x+6 is 22/3