What is the integral from 2 to 4 of 4(3x-1) ?

The integral from 2 to 4 of 4(3x-1) is 64

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integral from 2 to 4 of 4(3x-1)

\int_{2}^{4} 4 (3 x - 1) d x

64

Solution steps

\int_{2}^{4} 4 (3 x - 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{2}^{4} 3 x - 1 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

= 4 (\int_{2}^{4} 3 x d x - \int_{2}^{4} 1 d x)

\int_{2}^{4} 3 x d x = 18

\int_{2}^{4} 1 d x = 2

= 4 (18 - 2)

Simplify

= 64

y^{^{''}} - 100 y = 0

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

4 y^{^{'}} - 12 x^{2} = 0

\frac{\partial}{\partial x} (x sin^{2} (x y - y))

\int \frac{3}{4 x} d x

What is the integral from 2 to 4 of 4(3x-1) ?
The integral from 2 to 4 of 4(3x-1) is 64