What is the integral from 1 to 7 of (x^2-8x+16)^2 ?

The integral from 1 to 7 of (x^2-8x+16)^2 is 486/5

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integral from 1 to 7 of (x^2-8x+16)^2

\int_{1}^{7} (x^{2} - 8 x + 16)^{2} d x

\frac{486}{5}

Decimal

97.2

Solution steps

\int_{1}^{7} (x^{2} - 8 x + 16)^{2} d x

Expand

(x^{2} - 8 x + 16)^{2} : x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256

= \int_{1}^{7} x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256 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_{1}^{7} x^{4} d x - \int_{1}^{7} 16 x^{3} d x + \int_{1}^{7} 96 x^{2} d x - \int_{1}^{7} 256 x d x + \int_{1}^{7} 256 d x

\int_{1}^{7} x^{4} d x = \frac{16806}{5}

\int_{1}^{7} 16 x^{3} d x = 9600

\int_{1}^{7} 96 x^{2} d x = 10944

\int_{1}^{7} 256 x d x = 6144

\int_{1}^{7} 256 d x = 1536

= \frac{16806}{5} - 9600 + 10944 - 6144 + 1536

Simplify

\frac{16806}{5} - 9600 + 10944 - 6144 + 1536 : \frac{486}{5}

= \frac{486}{5}

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What is the integral from 1 to 7 of (x^2-8x+16)^2 ?
The integral from 1 to 7 of (x^2-8x+16)^2 is 486/5