[3] (a) Evaluate dx (b) Determine if the following integrals are convergent or divergent. Evaluate if convergent. -√x (i) So exxx dx ိ (ii) √4 6-vx dx √x

4.  Determine whether the improper integral converges and, if so, evaluate it. (If the quantity diverges, enter DIVERGES.) ∞ 04x dx(3 + x2)2   please show step by step  clearly.

Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule of derivatives.

Decide whether or not the given integral converges.   +∞ 4 x1.5  dx   1