What is the integration of Sin inverse X?

The integral of sin inverse is given by x sin-1x + √(1 – x2) + C, where C is the constant of integration. Mathematically, the sin inverse integral is written as ∫arcsin x dx = ∫sin-1x dx = x sin-1x + √(1 – x2) + C. Integral of sin inverse x is also called the antiderivative of sin inverse x.

What is the derivative of sin inverse root X?

Examples on Derivative of Sin Inverse x Solution: The derivative of sin inverse x is 1/√(1-x2), where -1 < x < 1.

What is the derivative of log X X?

The derivative is f'(x)=1−logxx2 . This is an example of the the Quotient Rule: Quotient Rule .

What is the root of sine?

The word “sine” (Latin “sinus”) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.

How to find the integral of X sine inverse of X?

The integral of x sine inverse of x is of the form. I = ∫ x sin – 1 x d x. Here the first function is sin – 1 x and the second function is x. I = ∫ sin – 1 x ⋅ x d x – – – ( i) Using the formula for integration by parts, we have. ∫ [ f ( x) g ( x)] d x = f ( x) ∫ g ( x) d x – ∫ [ d d x f ( x) ∫ g ( x) d x] d x.

Why is sin(x^2) not integrable?

Originally Answered: Why sin (x^2) is not integrable? There are a few different ways you can interpret the question. 1. You can say a function on the real numbers is integrable if the definite integral exists. In the case of this function, this integral clearly diverges.

Why does the inverse of a function exist?

When , the function is undefined (check it!), so is rejected. For , it seems like everything is defined. And since this function is approximately equal to , this is one to one and onto. Hence an inverse exists. And the ones who have seen me solve integrals using this trick, already know what follows next…..