I need to compute $$\mathbb{E}\left[X^n|X>c\right]$$
I am quite sure that I can rewrite as: $$\mathbb{E}\left[X^n|X>c\right]=\frac{\mathbb E\left[X^nI_{X>c}\right]}{P(X>c)}$$
However, I am not so sure on how I should contine. My guess is that $\mathbb E\left[X^nI_{X>c}\right]$ should be $$ \int_{-\infty}^{+\infty} x^nI_{x>c}f(x)dx=\int_c^{+\infty}x^nf(x)dx$$
And the final solution: $$\frac{\int_c^{+\infty}x^nf(x)dx}{P(X>c)}$$ But I am not so sure, could some of you kindly help me?
Moreover, in the case I want to change variables and suppose that $c=F^{-1}(K)$, could you give me a hint about that?