Maharashtra Board Solutions for Chapter: Mathematical Methods, Exercise 2: Exercises

The magnitude of vector product of two unit vectors making an angle 60 with each other

Given ${\overrightarrow{V}}_1 = 5i+2j and {\overrightarrow{V}}_2 =ai-6j$are perpendicular to each other determine the value of a.

Obtain the derivative for the following functions:

$\left(i\right) x \sin x$

Obtain the derivative for the following functions:

$\left(ii\right) x^4 +\cos x$

Obtain derivative of the following function

$\left(iii\right) \frac{x}{\sin x}$

Using the rule for differentiation for the quotient of two functions, prove that $\frac{d}{dx}\left(\frac{\sin x}{\cos x}\right) =se{c}^{2}x$

Evaluate the following integral:

${\int }_0^{\pi /2}\sin x dx$.

Evaluate the following integral ${\int }_1^{5}xdx$