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人気のある微分積分 >

integral from 0 to 2pi of-4cos^2(t)

解

\int_{0}^{2 π} - 4 cos^{2} (t) d t

解

- 4 π

+1

十進法表記

- 12.56637 \dots

解答ステップ

\int_{0}^{2 π} - 4 cos^{2} (t) d t

定数を除く:

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

= - 4 \cdot \int_{0}^{2 π} cos^{2} (t) d t

三角関数の公式を使用して書き換える

= - 4 \cdot \int_{0}^{2 π} \frac{1 + cos ( 2 t )}{2} d t

定数を除く:

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

= - 4 \cdot \frac{1}{2} \cdot \int_{0}^{2 π} 1 + cos (2 t) d t

総和規則を適用する:

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

= - 4 \cdot \frac{1}{2} (\int_{0}^{2 π} 1 d t + \int_{0}^{2 π} cos (2 t) d t)

\int_{0}^{2 π} 1 d t = 2 π

\int_{0}^{2 π} cos (2 t) d t = 0

= - 4 \cdot \frac{1}{2} (2 π + 0)

簡素化

- 4 \cdot \frac{1}{2} (2 π + 0) : - 4 π

= - 4 π

グラフ

人気の例

integral from 3 to 5 of x/(x^2+4x+13)

\int_{3}^{5} \frac{x}{x ^{2} + 4 x + 13} d x

integral from 2 to 4 of x^{2x}(1+ln(x))

\int_{2}^{4} x^{2 x} (1 + ln (x)) d x

integral from 2 to 4 of x^2+2x

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

integral from-3 to 1 of x^2

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

integral from 1 to 4 of (2x-4/(x^2))

\int_{1}^{4} (2 x - \frac{4}{x ^{2}}) d x