What is the integral from-4 to 2 of-(y^2)/2-y+4 ?

The integral from-4 to 2 of-(y^2)/2-y+4 is 18

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integral from-4 to 2 of-(y^2)/2-y+4

\int_{- 4}^{2} - \frac{y ^{2}}{2} - y + 4 d y

18

Solution steps

\int_{- 4}^{2} - \frac{y ^{2}}{2} - y + 4 d y

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}^{2} \frac{y ^{2}}{2} d y - \int_{- 4}^{2} y d y + \int_{- 4}^{2} 4 d y

\int_{- 4}^{2} \frac{y ^{2}}{2} d y = 12

\int_{- 4}^{2} y d y = - 6

\int_{- 4}^{2} 4 d y = 24

= - 12 - (- 6) + 24

Simplify

= 18

f (x) = \frac{x ^{5}}{7}

\int cos (2 x - 2) d x

\int \frac{x ^{4}}{9 - x ^{5}} d x

y^{^{'}} = e^{- x} y

y^{^{''}} - 3 y^{^{'}} - 10 y = - 3 x^{2} e^{- 6 x}

What is the integral from-4 to 2 of-(y^2)/2-y+4 ?
The integral from-4 to 2 of-(y^2)/2-y+4 is 18