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

Lösung

\int_{- 1}^{0} (1 - x) cos (nπ x) d x

- \frac{1 - ( - 1 ) ^{n}}{π ^{2} n ^{2}}

Schritte zur Lösung

\int_{- 1}^{0} (1 - x) cos (nπ x) d x

Multipliziere aus

(1 - x) cos (nπ x) : cos (πn x) - x cos (πn x)

= \int_{- 1}^{0} cos (πn x) - x cos (πn x) d x

Wende die Summenregel an:

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

= \int_{- 1}^{0} cos (πn x) d x - \int_{- 1}^{0} x cos (πn x) d x

\int_{- 1}^{0} cos (πn x) d x = 0

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

= 0 - \frac{1 - ( - 1 ) ^{n}}{π ^{2} n ^{2}}

Vereinfache

= - \frac{1 - ( - 1 ) ^{n}}{π ^{2} n ^{2}}

\int_{0}^{1} x^{2} y e^{x y} d x

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\int_{0}^{1} \frac{2}{( 5 + 3 x ) ^{\frac{1}{2}}} d x

\int_{- 4}^{4} - x^{2} + 16 d x