Integrate \(\frac{1 + x}{x^{3}} \mathrm d x\)

Evaluate \(\int_{0} ^{\frac{\pi}{2}} \sin x \mathrm d x\)

P, Q, and R are subsets of the universal set U. The Venn diagram showing the relationship \((P \cap Q) \cup R\) is

If the angle of a sector of a circle with radius 10.5 cm is 120°, find the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)]

Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)