What is the integral of 10^3sqrt(x^2) ?

The integral of 10^3sqrt(x^2) is 500x^2+C

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integral of 10^3sqrt(x^2)

\int 1 0^{3} x^{2} d x

500 x^{2} + C

Solution steps

\int 1 0^{3} x^{2} d x

Take the constant out:

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

= 1 0^{3} \cdot \int x^{2} d x

Simplify

= 1000 \cdot \int x^{2} d x

x^{2} = (x),

assuming

x \geq 0

= 1000 \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 1000 \cdot \frac{x ^{2}}{2}

Simplify

1000 \cdot \frac{x ^{2}}{2} : 500 x^{2}

= 500 x^{2}

Add a constant to the solution

= 500 x^{2} + C

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What is the integral of 10^3sqrt(x^2) ?
The integral of 10^3sqrt(x^2) is 500x^2+C