Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …

Numerically it seems to be true that $$ \int_0^\infty \frac {\sin x} {\sqrt {x}}dx=\sqrt {\frac {\pi} {2}}. $$ Any ideas how to prove this?

不定积分计算器 可以用分析整合的方法，计算出一个给定变量的函数的不定积分（原函数）。 它也可以画出函数和它的原函数的图像。 请注意，计算的不定积分属于一类函数F (x) C，其中C …

Functional Cookies are used to record your choices and settings regarding our Services, maintain your preferences over time and recognize you when you return to our Services. These …

2017年7月17日 · I asked my professor for the integration of $\sqrt {x} \sin x$ but he said that this is not in our syllabus. I tried on my own by substitution and by parts but it gets more complicated.

General solution : \displaystyle {x}= {\left ( {2} {n}\cdot\pi+\frac {\pi} { {4}}\right)} {\quad\text {and}\quad} {x}= {\left ( {2} {n}\cdot\pi+\frac { { {3}\pi}} { {4}}\right)} Explanation: \displaystyle {2} …

I_n=\frac {\sin x\cos^ {n-1} x}n+\frac {n-1}nI_ {n-2} \int_0^ {\frac {\pi}2}\sin^n\theta\mathrm {d}\theta=\int_0^ {\frac {\pi}2}\cos^n\theta\mathrm {d}\theta=\frac {\sqrt\pi\,\Gamma\left (\dfrac …

\sin^ {2} {\frac {\theta} {2}} = \frac {1 - \cos {\theta}} {2} \\ \sin {\frac {\theta} {2}} = \pm \sqrt {\frac {1 - \cos {\theta}} {2}} \\ \cos^ {2} {\frac {\theta} {2}} = \frac {1 + \cos {\theta}} {2} \\ \cos {\frac …

$$\int \sqrt {\sin x}\ \operatorname dx$$ I asked my teachers and they said that this integration is pretty next level and will be taught in college. Can anyone help?

Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.