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

The integral from 1 to 4 of k(x^2+1) is 24k

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

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

24 k

Solution steps

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

Take the constant out:

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

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

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

\int_{1}^{4} x^{2} d x = 21

= k (3 + 21)

Simplify

= 24 k

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What is the integral from 1 to 4 of k(x^2+1) ?
The integral from 1 to 4 of k(x^2+1) is 24k