What is the integral from 0 to 2 of 4x ?

The integral from 0 to 2 of 4x is 8

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integral from 0 to 2 of 4x

\int_{0}^{2} 4 x d x

8

Solution steps

\int_{0}^{2} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{0}^{2} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{2}

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

Compute the boundaries:

2

= 4 \cdot 2

Simplify

= 8

x \to 1 lim (1 - x)

y^{^{''}} + 16 y = csc^{2} (4 t)

\int_{1}^{9} \frac{2}{x ^{3}} d x

\int \frac{1}{( 16 t ^{2} + 9 ) ^{2}} d t