What is the integral from 0 to 2 of 4t^7 ?

The integral from 0 to 2 of 4t^7 is 128

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integral from 0 to 2 of 4t^7

\int_{0}^{2} 4 t^{7} d t

128

Solution steps

\int_{0}^{2} 4 t^{7} d t

Take the constant out:

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

= 4 \cdot \int_{0}^{2} t^{7} d t

Apply the Power Rule

: [\frac{t ^{8}}{8}]_{0}^{2}

= 4 [\frac{t ^{8}}{8}]_{0}^{2}

Compute the boundaries:

32

= 4 \cdot 32

Simplify

= 128

\int (\frac{x ^{2} - 1}{x ^{\frac{3}{2}}}) d x

\int_{0}^{\frac{π}{6}} sin^{2} (x) d x

x \to 0 lim (\frac{5 ^{x} - 1 0 ^{x}}{x})

x \to 5 lim (x^{3} + 2 x)

\int \frac{1}{2 ( x ^{3} + x ^{2} )} d x

What is the integral from 0 to 2 of 4t^7 ?
The integral from 0 to 2 of 4t^7 is 128