What is the integral from 1 to 5 of 8x ?

The integral from 1 to 5 of 8x is 96

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integral from 1 to 5 of 8x

\int_{1}^{5} 8 x d x

96

Solution steps

\int_{1}^{5} 8 x d x

Take the constant out:

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

= 8 \cdot \int_{1}^{5} x d x

Apply the Power Rule

= 8 [\frac{x ^{2}}{2}]_{1}^{5}

Compute the boundaries:

12

= 8 \cdot 12

Simplify

= 96

\int_{2}^{x} cos (t) d t

x \to 2 lim (x^{2} + 4 x - 12)

\frac{d}{d x} (- \frac{72}{( x + 2 ) ^{4}})

\frac{d}{d x} (e + ln (x))

x \to 0 lim (3 - 2^{x})