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人気のある微分積分 >

integral of 1/2 cos^2(3θ)

解

\int \frac{1}{2} cos^{2} (3 θ) d θ

解

\frac{1}{4} (θ + \frac{1}{6} sin (6 θ)) + C

解答ステップ

\int \frac{1}{2} cos^{2} (3 θ) d θ

定数を除く:

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

= \frac{1}{2} \cdot \int cos^{2} (3 θ) d θ

三角関数の公式を使用して書き換える

= \frac{1}{2} \cdot \int \frac{1}{2} (1 + cos (6 θ)) d θ

定数を除く:

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

= \frac{1}{2} \cdot \frac{1}{2} \cdot \int 1 + cos (6 θ) d θ

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

= \frac{1}{2} \cdot \frac{1}{2} (\int 1 d θ + \int cos (6 θ) d θ)

\int 1 d θ = θ

\int cos (6 θ) d θ = \frac{1}{6} sin (6 θ)

= \frac{1}{2} \cdot \frac{1}{2} (θ + \frac{1}{6} sin (6 θ))

簡素化

\frac{1}{2} \cdot \frac{1}{2} (θ + \frac{1}{6} sin (6 θ)) : \frac{1}{4} (θ + \frac{1}{6} sin (6 θ))

= \frac{1}{4} (θ + \frac{1}{6} sin (6 θ))

定数を解答に追加する

= \frac{1}{4} (θ + \frac{1}{6} sin (6 θ)) + C

グラフ

人気の例

integral of r^2(r^3-4)^7

\int r^{2} (r^{3} - 4)^{7} d r

derivative xy+x

d er i v a t i v e x y + x

tangent f(x)= 6/(x^2),(1,6)

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derivative of (f(x(3x))^2-4)

\frac{d}{d x} ((f (x) (3 x))^{2} - 4)

integral from pi/3 to pi of sin(x)

\int_{\frac{π}{3}}^{π} sin (x) d x