Recent questions tagged q7

Integrate the function\[x\;\sin^{-1}x\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in the area lying between the curves $y^2 = 4x$ and $y = 2x$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area enclosed by the parabola $4y = 3x^2$ and the line $2y = 3x + 12.$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{1+3x-x^2}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\tan x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the smaller part of the circle $x^2 + y^2 = a^2$ cut off by the line $x =\Large { \frac{a}{\sqrt 2}}$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution\[\int\limits_{-1}^1\frac{dx}{x^2+2x+5}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^1x\;(1-x)^n\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\large\int\frac{\sin x}{\sin(x-a)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $xy=\log\: y+C\qquad:y'=\large\frac{y^2}{1-xy}$$\;(xy\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of parabolas having vertex at origin at axis along positive y-axis.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $y\;\log\: y\;dx-x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

The cartesian equation of a line is $\frac{\large x-5}{\large 3} = \frac{\large y+4}{\large 7} = \frac{\large z-6}{\large 2}$. Write its vector form.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

What does $\sin^{-1} \frac{5}{13}+\cos^{-1} \frac {3}{5}$ reduce to?

asked Nov 29, 2012 by vaishali.a

1 answer

$If \; A^{-1}=\begin{bmatrix} 3 &-1 & 1\\ -15&6 &-5 \\ 5& -2&2 \end{bmatrix} \; and \; B = \begin{bmatrix} 1 & 2 & -2\\ -1 & 3 & 0\\ 0 & -2 & 1 \end{bmatrix}, \; find \; (AB)^{-1} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: <br>$5x+2y=4 $<br>$7x+3y = 5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the minimum of $Z$ occurs at more than two points. Minimise and Maximise $Z = 5x + 10 y$ subject to $x + 2y \leq 120, x + y \geq 60, x – 2y \geq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the general solution of the differential equation$\large\frac{dy}{dx}+\large\frac{y^2+y+1}{x^2+x+1}=0$ is given by $(x+y+1)\;=\;A(1-x-y-2xy)$, where A is parameter

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the value of $x$, if $ \begin{vmatrix} 2&4 \\ 5&1 \end{vmatrix} = \begin{vmatrix} 2x&4 \\ 6&x \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following: $sec^{-1} \bigg( \frac {2} {\sqrt 3} \bigg) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the intervals in which the function $f$ given by $f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0$ is $(i) \;increasing\qquad (ii) \;decreasing.$

asked Nov 28, 2012 by thanvigandhi_1

1 answer