What is the integral from-3 to 4 of y-(y^2-12) ?

The integral from-3 to 4 of y-(y^2-12) is 343/6

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integral from-3 to 4 of y-(y^2-12)

\int_{- 3}^{4} y - (y^{2} - 12) d y

\frac{343}{6}

Decimal Notation

57.16666 \dots

Solution steps

\int_{- 3}^{4} y - (y^{2} - 12) d y

Simplify

= \int_{- 3}^{4} y - y^{2} + 12 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_{- 3}^{4} y d y - \int_{- 3}^{4} y^{2} d y + \int_{- 3}^{4} 12 d y

\int_{- 3}^{4} y d y = \frac{7}{2}

\int_{- 3}^{4} y^{2} d y = \frac{91}{3}

\int_{- 3}^{4} 12 d y = 84

= \frac{7}{2} - \frac{91}{3} + 84

Simplify

\frac{7}{2} - \frac{91}{3} + 84 : \frac{343}{6}

= \frac{343}{6}

(- 1, 6), (7, - 2)

x \to 2 - lim (\frac{2}{x ^{2} - 4})

\frac{d y}{d x}, x^{3} y^{5} + 3 x = 8 y^{3} + 1

\int_{0}^{1} \frac{x}{( 2 - x ) ^{2}} d x

\frac{d y}{d x} = x (y - 1)

What is the integral from-3 to 4 of y-(y^2-12) ?
The integral from-3 to 4 of y-(y^2-12) is 343/6