LadiesMan said:How do I find the anti-derivative of:
[tex]\int sin^{3/2}x dx[/tex]
I can't see where to start...
Thanks
An antiderivative is the inverse operation of differentiation. It is a function that, when differentiated, gives back the original function.
The general formula for the antiderivative of (sin x)^3/2 is (2/3)(sin x)^(5/2) + C, where C is the constant of integration.
To find the antiderivative of (sin x)^3/2, you can use the power rule for integration, which states that the antiderivative of x^n is (1/(n+1))x^(n+1) + C. In this case, n = 3/2, so the antiderivative is (2/3)(sin x)^(5/2) + C.
Yes, the antiderivative of (sin x)^3/2 can be expressed in terms of elementary functions. In this case, the elementary function is the sine function.
(sin x)^3/2 is a commonly used function in calculus, and its antiderivative can be used to solve various integrals involving trigonometric functions. It also has applications in physics and engineering, such as in the calculation of arc lengths and areas under curves.