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人気のある微分積分 >

integral from 0 to sin(z) of x-1

解

\int_{0}^{s i n (z)} x - 1 d x

解

\frac{sin ^{2} ( z )}{2} - sin (z)

解答ステップ

\int_{0}^{s i n (z)} x - 1 d x

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

= \int_{0}^{s i n (z)} x d x - \int_{0}^{s i n (z)} 1 d x

\int_{0}^{s i n (z)} x d x = \frac{sin ^{2} ( z )}{2}

\int_{0}^{s i n (z)} 1 d x = sin (z)

= \frac{sin ^{2} ( z )}{2} - sin (z)

人気の例

integral from 1 to 2 of (2x)/((x^2+1)^2)

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

integral from-pi/6 to pi/6 of tan^3(x)

\int_{- \frac{π}{6}}^{\frac{π}{6}} tan^{3} (x) d x

integral from-pi to 0 of (pi+x)

\int_{- π}^{0} (π + x) d x

integral from-1 to 1 of (8-|x|)

\int_{- 1}^{1} (8 - ∣ x ∣) d x

integral from 1 to 3 of 2xcos(x^2)

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