What is the integral from 0 to 1 of (7-21/2 x)^2 ?

The integral from 0 to 1 of (7-21/2 x)^2 is 49/4

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integral from 0 to 1 of (7-21/2 x)^2

\int_{0}^{1} (7 - \frac{21}{2} x)^{2} d x

\frac{49}{4}

Solution steps

\int_{0}^{1} (7 - \frac{21}{2} x)^{2} d x

Simplify

(7 - \frac{21}{2} x)^{2} : 49 - 147 x + \frac{441}{4} x^{2}

= \int_{0}^{1} 49 - 147 x + \frac{441}{4} 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

= \int_{0}^{1} 49 d x - \int_{0}^{1} 147 x d x + \int_{0}^{1} \frac{441}{4} x^{2} d x

\int_{0}^{1} 49 d x = 49

\int_{0}^{1} 147 x d x = \frac{147}{2}

\int_{0}^{1} \frac{441}{4} x^{2} d x = \frac{147}{4}

= 49 - \frac{147}{2} + \frac{147}{4}

Simplify

49 - \frac{147}{2} + \frac{147}{4} : \frac{49}{4}

= \frac{49}{4}

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What is the integral from 0 to 1 of (7-21/2 x)^2 ?
The integral from 0 to 1 of (7-21/2 x)^2 is 49/4