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

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

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

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

2

Solution steps

\int_{\frac{1}{2}}^{\frac{3}{2}} - 2 x + 4 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_{\frac{1}{2}}^{\frac{3}{2}} 2 x d x + \int_{\frac{1}{2}}^{\frac{3}{2}} 4 d x

\int_{\frac{1}{2}}^{\frac{3}{2}} 2 x d x = 2

\int_{\frac{1}{2}}^{\frac{3}{2}} 4 d x = 4

= - 2 + 4

Simplify

= 2

\int (2 x - 5) e^{x^{2} - 5 x} d x

\frac{d y}{d x} + 2 x y = 0

\int_{- 3}^{0} (2 + 9 - x^{2}) d x

n = 0 \sum \infty n e^{- 2 n}

x \to \infty lim (- \frac{10}{x})

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