What is the integral from 0 to 0.1 of 400x ?

The integral from 0 to 0.1 of 400x is 2

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integral from 0 to 0.1 of 400x

\int_{0}^{0.1} 400 x d x

2

Solution steps

\int_{0}^{0.1} 400 x d x

Take the constant out:

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

= 400 \cdot \int_{0}^{0.1} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{0.1}

= 400 [\frac{x ^{2}}{2}]_{0}^{0.1}

Simplify

= 400 [0.5 x^{2}]_{0}^{0.1}

Compute the boundaries:

0.005

= 400 \cdot 0.005

Simplify

= 2

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\int_{- 2}^{2} x (x^{2} - 9) d x

\int_{0}^{2} (x^{3} + 4 x) d x

What is the integral from 0 to 0.1 of 400x ?
The integral from 0 to 0.1 of 400x is 2