Question

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5),(3, 6)} is a function from A to B. State whether f is one-one or not.

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$

Evaluate $\textstyle\int{\frac{\cos{\sqrt{x}}}{\sqrt{x}}}\,d x\ .$

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.