1. Evaluate the following integrals a. ∫ √𝑥𝑑�

The integral of √x dx can be solved as follows:

First, rewrite √x as x^(1/2).

So, we have ∫ x^(1/2) dx.

The power rule for integration states that ∫ x^n dx = (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Applying this rule, we get:

(1/(1/2 + 1))x^(1/2 + 1) + C

Simplify this to:

(2/3)x^(3/2) + C

So, ∫ √x dx = (2/3)x^(3/2) + C.