**I. Integrate the following functions w.r.t. x:**

**(i) + – x + 1Solution:**

Solution:

Solution:

Solution:

Solution:

**II. Evaluate:**

**(i) ∫ta x . dxSolution:**

Solution:

Solution:

Solution:

**Solution:**= -cot x – tan x + c

Solution:

Solution:

Solution:

Solution:

**(x) ∫sin 4x cos 3x dxSolution:**

**III. Evaluate:**

**(i) ∫⋅dxSolution:**

Solution:

**Solution:**

Solution:

Solution:

Solution:

Solution:

**(viii) ∫ x . dxSolution:**

Solution:

Solution:

**IV.**

**Question 1.Solution:**

By the definition of integral,