Question

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Evaluate : $\textstyle\int$ cos⁻¹(sin x) dx.

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

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

If A is square matrix of order 3 such that $|a d j A|=$ 64, find $|A|.$

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