What is the integral from 7 to 8 of-7log_{2}(t) ?

The integral from 7 to 8 of-7log_{2}(t) is -(7(24ln(2)-1-7ln(7)))/(ln(2))

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integral from 7 to 8 of-7log_{2}(t)

\int_{7}^{8} - 7 lo g_{2} (t) d t

- \frac{7 ( 24 ln ( 2 ) - 1 - 7 ln ( 7 ) )}{ln ( 2 )}

Decimal

- 20.34074 \dots

Solution steps

\int_{7}^{8} - 7 lo g_{2} (t) d t

Take the constant out:

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

= - 7 \cdot \int_{7}^{8} lo g_{2} (t) d t

Apply Integration By Parts

: [t lo g_{2} (t) - \int \frac{1}{ln ( 2 )} d t]_{7}^{8}

= - 7 [t lo g_{2} (t) - \int \frac{1}{ln ( 2 )} d t]_{7}^{8}

\int \frac{1}{ln ( 2 )} d t = \frac{1}{ln ( 2 )} t

= - 7 [t lo g_{2} (t) - \frac{1}{ln ( 2 )} t]_{7}^{8}

Join

t lo g_{2} (t) - \frac{1}{ln ( 2 )} t : \frac{- t + t ln ( t )}{ln ( 2 )}

= - 7 [\frac{- t + t ln ( t )}{ln ( 2 )}]_{7}^{8}

Compute the boundaries:

\frac{24 ln ( 2 ) - 1 - 7 ln ( 7 )}{ln ( 2 )}

= - 7 \cdot \frac{24 ln ( 2 ) - 1 - 7 ln ( 7 )}{ln ( 2 )}

Simplify

= - \frac{7 ( 24 ln ( 2 ) - 1 - 7 ln ( 7 ) )}{ln ( 2 )}

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What is the integral from 7 to 8 of-7log_{2}(t) ?
The integral from 7 to 8 of-7log_{2}(t) is -(7(24ln(2)-1-7ln(7)))/(ln(2))