d/dx∫baarcsin xdx=()A.0 D.arcsin b-arcsina

d/dx∫baarcsin xdx=()A.0 D.arcsin b-arcsina

To solve the problem of finding $\frac{d}{dx} \int_{a}^{b} \arcsin x \, dx$, we start by analyzing the nature of the integral. The integral $\int_{a}^{b} \arcsin x \, dx$ has constant limits of integration ($a$ and $b$) and integrates the function $\arcsin x$ with respect to $x$. When integrating a function over a fixed interval with constant bounds, the result is a numerical constant (not a function of $x$).

The derivative of a constant with respect to any variable is always zero. Since $\int_{a}^{b} \arcsin x \, dx$ evaluates to a constant (independent of $x$), its derivative with respect to $x$ is $0$.

Answer: A.0