What is the integral from-1/2 to 0 of (1/2+2y+3z) ?

The integral from-1/2 to 0 of (1/2+2y+3z) is (3z)/2

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integral from-1/2 to 0 of (1/2+2y+3z)

\int_{- \frac{1}{2}}^{0} (\frac{1}{2} + 2 y + 3 z) d y

\frac{3 z}{2}

Solution steps

\int_{- \frac{1}{2}}^{0} \frac{1}{2} + 2 y + 3 z d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{1}{2}}^{0} \frac{1}{2} d y + \int_{- \frac{1}{2}}^{0} 2 y d y + \int_{- \frac{1}{2}}^{0} 3 z d y

\int_{- \frac{1}{2}}^{0} \frac{1}{2} d y = \frac{1}{4}

\int_{- \frac{1}{2}}^{0} 2 y d y = - \frac{1}{4}

\int_{- \frac{1}{2}}^{0} 3 z d y = \frac{3 z}{2}

= \frac{1}{4} - \frac{1}{4} + \frac{3 z}{2}

Simplify

= \frac{3 z}{2}

\frac{\partial}{\partial x} (e^{x s i n (y)})

1 + 2 x

x \to 2 lim (\frac{3 x + 4}{8 x - 1})

\int \frac{1}{u 3 - u ^{2}} d u

\int x x^{'} d x

What is the integral from-1/2 to 0 of (1/2+2y+3z) ?
The integral from-1/2 to 0 of (1/2+2y+3z) is (3z)/2