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Homework Statement
Intergrate arcsinx
Homework Equations
The Attempt at a Solution
I couldn't even touch this question. I saw the answer but still can not understand how to do this.
The formula for integrating arcsinx is ∫arcsinx dx = xarcsinx - √(x^2 - 1) + C.
The integration formula for arcsinx can be proved using integration by parts and trigonometric identities, specifically the double angle formula for sine.
The domain of arcsinx is [-1, 1] and the range is [-π/2, π/2].
Yes, the integration of arcsinx can be solved using the substitution method, specifically by substituting u = sinx.
Yes, the integration of arcsinx is used in various fields such as physics, engineering, and signal processing. It is used to calculate the surface area of a spherical cap, find the arc length of a circle segment, and analyze signals in communication systems.