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

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

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integral from y to 1 of 3x

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

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

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

f (4 k) = x^{2} - 2 x

\int \frac{17 - 17 x}{1 - x} d x

\frac{d}{d x} (ln (x^{2} + y^{2} + z^{2}))

\frac{d}{d x} (lo g_{10} (x^{2} + y))

\frac{\partial}{\partial x} (- 2 e^{- x^{2} - y^{2}} x cos (x y) - e^{- x^{2} - y^{2}} y sin (x y))

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