What is the integral from 0 to 3/2 of cos(pix) ?

The integral from 0 to 3/2 of cos(pix) is -1/pi

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integral from 0 to 3/2 of cos(pix)

\int_{0}^{\frac{3}{2}} cos (π x) d x

- \frac{1}{π}

Decimal

- 0.31830 \dots

Solution steps

\int_{0}^{\frac{3}{2}} cos (π x) d x

Apply u-substitution

: \int_{0}^{\frac{3 π}{2}} cos (u) \frac{1}{π} d u

= \int_{0}^{\frac{3 π}{2}} cos (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int_{0}^{\frac{3 π}{2}} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{π} [sin (u)]_{0}^{\frac{3 π}{2}}

Compute the boundaries:

- 1

= \frac{1}{π} (- 1)

Simplify

= - \frac{1}{π}

y^{^{'}} = e^{x}

\frac{\partial}{\partial y} (\frac{4 y}{x})

\frac{\partial}{\partial y} ((2 x + 3) (y - 2))

\frac{d}{d x} (2 e^{2 x} - e^{- x})

\frac{3}{4} x^{8}

What is the integral from 0 to 3/2 of cos(pix) ?
The integral from 0 to 3/2 of cos(pix) is -1/pi