Question

Evaluate $\textstyle\int$ sin³ x dx.

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

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

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 $a_{32}$.

If matrix A = $\left(\begin{array}{l l }1 & -1 \\ -1 & 1\end{array}\right)$ and A² = kA, then write the value of k.

If the following function f(x) is continuous at x = 0, then write the value of k.

Write the value of λ so that the vectors $\stackrel{\rightarrow}{a}\$ = $2 \stackrel{\wedge}{i}+λ\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are perpendicular to each other ?