Question

Find : $\int{\frac{\sin^{2}x-\cos^{2}x}{\sin x\cos x}}\,d x$

Find x from the matrix equation $\left(\begin{array}{l l }1 & 3 \\ 4 & 5\end{array}\right)$ $\left(\begin{array}{l }x \\ 2\end{array}\right)$ = $\left(\begin{array}{l }5 \\ 6\end{array}\right)$ .

Evaluate: $\textstyle\int(1-x){\sqrt{x}}\,d x~.$

Evaluate $\textstyle\int$$\frac{x^{3}-1}{x^{2}}d x.$

The elements $a_{i j}$ of a 3 × 3 matrix are given by $a_{i j}=\,\frac{1}{2}\,\vert-3i+j\vert.$. Write the value of element $a_{32}$.

For a 2 × 2 matrix A = [ $a_{i j}$ ], whose elements are given by $a_{i j}=\,{\frac{(i+2j)^{2}}{4}}$ , write the value of $a_{\mathrm{21}}$.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.