What is the integral from 1 to 4 of f(x+5) ?

The integral from 1 to 4 of f(x+5) is 45/2 f

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integral from 1 to 4 of f(x+5)

\int_{1}^{4} f (x + 5) d x

\frac{45}{2} f

Solution steps

\int_{1}^{4} f (x + 5) d x

Take the constant out:

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

= f \cdot \int_{1}^{4} 5 + 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

= f (\int_{1}^{4} 5 d x + \int_{1}^{4} x d x)

\int_{1}^{4} 5 d x = 15

\int_{1}^{4} x d x = \frac{15}{2}

= f (15 + \frac{15}{2})

Join

15 + \frac{15}{2} : \frac{45}{2}

= \frac{45}{2} f

What is the integral from 1 to 4 of f(x+5) ?
The integral from 1 to 4 of f(x+5) is 45/2 f