What is the integral from 1 to 2 of 3x^2 ?

The integral from 1 to 2 of 3x^2 is 7

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integral from 1 to 2 of 3x^2

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

7

Solution steps

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

Take the constant out:

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

= 3 \cdot \int_{1}^{2} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{2}

= 3 [\frac{x ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= 3 \cdot \frac{7}{3}

Simplify

= 7

\int \frac{1}{x ^{2} + 4 x + 3} d x

\int_{2}^{4} - x^{2} + 6 x - 8 d x

x \to - 8 - lim (\frac{x + 7}{x + 8})

cos (\frac{x}{2})

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

What is the integral from 1 to 2 of 3x^2 ?
The integral from 1 to 2 of 3x^2 is 7