What is the integral from 0 to 2 of 2t^3 ?

The integral from 0 to 2 of 2t^3 is 8

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integral from 0 to 2 of 2t^3

\int_{0}^{2} 2 t^{3} d t

8

Solution steps

\int_{0}^{2} 2 t^{3} d t

Take the constant out:

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

= 2 \cdot \int_{0}^{2} t^{3} d t

Apply the Power Rule

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

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

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

\frac{d}{d x} (x + y) = 2

8 t^{2} + 9

\int x^{2} e^{1 x} d x

\int \frac{e ^{x} + e ^{2 x}}{e ^{x}} d x

e^{- 2 t} sin (t)

What is the integral from 0 to 2 of 2t^3 ?
The integral from 0 to 2 of 2t^3 is 8