Q7 of 45 Page 1

Evaluate:

Let I =

This can be solved by applying method of substitution:

Let, x = sin θ

∴ θ = sin^-1 x …(1)

As, x = sin θ

⇒ dx = cos θ dθ

∴ I = {∵ 1 – sin²θ = cos² θ }

⇒ I =

∴ I = sin^-1 x + C {using equation 1}

If a matrix has 5 elements, write all possible orders it can have.

Evaluate:

Write the direction-cosines of the line joining the points (1, 0, 0) and (0, 1, 1)

Write the projection of the vector on the vector