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

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

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integral from-1/2 to 3/2 of x-cos(pix)

\int_{- \frac{1}{2}}^{\frac{3}{2}} x - cos (π x) d x

1

Solution steps

\int_{- \frac{1}{2}}^{\frac{3}{2}} x - cos (π x) d x

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}}^{\frac{3}{2}} x d x - \int_{- \frac{1}{2}}^{\frac{3}{2}} cos (π x) d x

\int_{- \frac{1}{2}}^{\frac{3}{2}} x d x = 1

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

= 1 - 0

Simplify

= 1

\int sin (x) cos (\frac{1}{2} x) d x

\frac{d y}{d x} = (- y)

\frac{d}{d x} ((2 - x) (x + 1)^{2})

x \to 0 lim (x - 1)

\int \frac{4 x ^{3} - 3 x ^{2} - 8 x}{6 x} d x

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