What is the integral from 0 to 2 of x^2+kx+1 ?

The integral from 0 to 2 of x^2+kx+1 is 8/3+k*2+2

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integral from 0 to 2 of x^2+kx+1

\int_{0}^{2} x^{2} + k x + 1 d x

\frac{8}{3} + k \cdot 2 + 2

Solution steps

\int_{0}^{2} x^{2} + k 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

= \int_{0}^{2} x^{2} d x + \int_{0}^{2} k x d x + \int_{0}^{2} 1 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} k x d x = k \cdot 2

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

= \frac{8}{3} + k \cdot 2 + 2

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What is the integral from 0 to 2 of x^2+kx+1 ?
The integral from 0 to 2 of x^2+kx+1 is 8/3+k*2+2