Question

For what value of x, the matrix $\left(\begin{array}{l l }1+x & 7 \\ 3-x & 8\end{array}\right)$ is a singular matrix ?

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$

Write fog, if f : R → R and g : R → R are given by f(x) = 8x³ and g(x) = $x^{1/3}.$

If $\stackrel{\rightarrow}{a}\$ =$4\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ =$2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ then find a unit vector parallel to the vector $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$

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 $a_{\mathrm{21}}$.

Evaluate $\textstyle\int$ sin³ x dx.

Find : $\textstyle\int{\frac{\sin^{6}x}{\cos^{8}x}}\,d x.$