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

The integral from x to 1 of 3x is (3(1-x^2))/2

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integral from x to 1 of 3x

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

\frac{3 ( 1 - x ^{2} )}{2}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2} - \frac{x ^{2}}{2}

= 3 (\frac{1}{2} - \frac{x ^{2}}{2})

Simplify

= \frac{3 ( 1 - x ^{2} )}{2}

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What is the integral from x to 1 of 3x ?
The integral from x to 1 of 3x is (3(1-x^2))/2