当n为奇数时，它是从1到n所有奇数相乘；当n为偶数时，它是从2到n所有偶数相乘。 证 \int_ {0}^ {\pi}f (\sin x)dx=\int_ {0}^ {\frac {\pi} {2}}f (\sin x)dx+\int_ {\frac {\pi} {2}}^ {\pi}f (\sin x)dx. 其中. \int_ {\frac {\pi} {2}}^ {\pi}f (\sin x)dx=\int_ {0}^ {\frac {\pi} {2}}f …

回到题目中的例子，如果我们考虑 \sin (dx) 作为一个微分形式的级数在一个闭区间上的定积分，那么 (dx)^ {k}=0,\,k\geq2 ，因此积分化作对 dx 的积分。 计算上和现有回答是一致的。 这么多回答竟然没有一个提到测度？ 把 \sin 当作一个测度，这就是一个良定义的表达式。 即： 其中 \sin 是一个测度。 测度就是给每一个（可测的）集合指定一个实数代表它的大小。 我们平常的积分都是在勒贝格测度上面积分的，它指定区间 (a,b) 的大小为 b -a 。 然而，没有什么可以阻止我们换一个 …

Integration is the opposite of differentiation basically. Integration helps us to determine the original function of a derivative if provided one. If $\frac {d (F (x))} {dx}=f (x)$, then $\int f (x)dx=F (x)+C$ . This is known as indefinite integrals. $\int f (x)dx$ will represent the complete class of integral.

Dec 18, 2022 · \begin{align} \int\frac1{sinx}dx&=\int\frac1{2sin\frac x2cos\frac x2}dx\\&=\int\frac{1}{2cos^2\frac x2tan\frac x2}dx\\&=\int\frac1{tan\frac x2}dtan\frac …

乘号和括号被额外放置 - 写 2sinx 相似的 2*sin(x) 数学函数和常数列表: • ln(x) — 自然对数. • sin(x) — 正弦. • cos(x) — 余弦. • tan(x) — 正切. • cot(x) — 余切. • arcsin(x) — 反正弦. • arccos(x) — 反余弦. • arctan(x) — 反正切. • arccot(x) — 反余切. • sinh(x) — 双 ...

\frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

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d/dx sin(x) d^2/dx^2 sin(x) int 1/(sin(x)) dx; method of washers; solve y'(x) = sin(x)

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I am working on trying to solve this problem: Prove: $\int \sin^n {x} \ dx = -\frac {1} {n} \cos {x} \cdot \sin^ {n - 1} {x} + \frac {n - 1} {n} \int \sin^ {n - 2} {x} \ dx$ Here are the steps that I fol...