What is the integral from x^2 to 4 of 3x ?

The integral from x^2 to 4 of 3x is 3(8-(x^4)/2)

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integral from x^2 to 4 of 3x

\int_{x^{2}}^{4} 3 x d x

3 (8 - \frac{x ^{4}}{2})

Solution steps

\int_{x^{2}}^{4} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{x^{2}}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{x^{2}}^{4}

= 3 [\frac{x ^{2}}{2}]_{x^{2}}^{4}

Compute the boundaries:

8 - \frac{x ^{4}}{2}

= 3 (8 - \frac{x ^{4}}{2})

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What is the integral from x^2 to 4 of 3x ?
The integral from x^2 to 4 of 3x is 3(8-(x^4)/2)