What is the integral from-1 to 0 of 1cos(npix) ?

The integral from-1 to 0 of 1cos(npix) is 0

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integral from-1 to 0 of 1cos(npix)

\int_{- 1}^{0} 1 cos (nπ x) d x

0

Solution steps

\int_{- 1}^{0} 1 \cdot cos (nπ x) d x

Apply Integration By Parts

: [x cos (πn x) - \int - πn x sin (πn x) d x]_{- 1}^{0}

= [x cos (πn x) - \int - πn x sin (πn x) d x]_{- 1}^{0}

\int - πn x sin (πn x) d x = x cos (πn x) - \frac{1}{πn} sin (πn x)

= [x cos (πn x) - (x cos (πn x) - \frac{1}{πn} sin (πn x))]_{- 1}^{0}

Simplify

= [\frac{1}{πn} sin (πn x)]_{- 1}^{0}

Compute the boundaries:

0

= 0

\int_{0}^{1} x^{2} (x - 1) d x

\int_{- 2}^{2} e^{2 x - 1} - e^{x} d x

\int_{- 1}^{1} (x^{99}) d x

\int_{0}^{4} e^{t} d t

\int_{x}^{0} e^{- 9 t} d t

What is the integral from-1 to 0 of 1cos(npix) ?
The integral from-1 to 0 of 1cos(npix) is 0