Question

Помогите пожалуйста найти Интеграл sinx d(sinx)

Answer 1

Неопределённый интеграл не зависит от переменной интегрирования.

Пусть sin(x) = u , тогда

$\int\limits {sin(x)} \, d(sin(x)) =\int\limits {u} \, du=u^{2} /2+C$

вернёмся к изначальной замене:

$\frac{sin^2(x)}{2} +C$

Answer 2

Finding the Integral of sin(x) d(sinx)

To find the integral of sin(x) d(sinx), we can use the substitution method. Let's proceed with the solution.

The integral of sin(x) d(sinx) can be found using the substitution method. We can substitute u = sin(x), and then d(sinx) becomes du. Therefore, the integral becomes the integral of u du, which is equal to (u^2)/2 + C, where C is the constant of integration.

So, the integral of sin(x) d(sinx) is (sin^2(x))/2 + C.