What is the integral from-1 to 3 of 30-3y^2-9/2 ?

The integral from-1 to 3 of 30-3y^2-9/2 is 74

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integral from-1 to 3 of 30-3y^2-9/2

\int_{- 1}^{3} 30 - 3 y^{2} - \frac{9}{2} d y

74

Solution steps

\int_{- 1}^{3} 30 - 3 y^{2} - \frac{9}{2} 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_{- 1}^{3} 30 d y - \int_{- 1}^{3} 3 y^{2} d y - \int_{- 1}^{3} \frac{9}{2} d y

\int_{- 1}^{3} 30 d y = 120

\int_{- 1}^{3} 3 y^{2} d y = 28

\int_{- 1}^{3} \frac{9}{2} d y = 18

= 120 - 28 - 18

Simplify

= 74

\frac{d y}{d x} = \frac{1}{1 + x ^{2}}

x \to 0 lim (\frac{5}{1 - e ^{\frac{1}{x}}})

16 y^{^{''}} + 11 y = 0

\int \frac{e ^{2 x}}{e ^{x} - 1} d x

\int_{0}^{1} \frac{x}{1 + x ^{2}} d x

What is the integral from-1 to 3 of 30-3y^2-9/2 ?
The integral from-1 to 3 of 30-3y^2-9/2 is 74