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

The integral from-1 to 1 of k(2x+4) is 8k

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

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

8 k

Solution steps

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

Take the constant out:

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

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

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

\int_{- 1}^{1} 4 d x = 8

\int_{- 1}^{1} 2 x d x = 0

= k (8 + 0)

Simplify

= 8 k

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What is the integral from-1 to 1 of k(2x+4) ?
The integral from-1 to 1 of k(2x+4) is 8k