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By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^\frac{\Large \pi}{\Large 2}\frac{\sin x-\cos x}{1+\sin x\cos x}\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^a\frac{\sqrt x}{\sqrt x+\sqrt{a-x}}dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^4\mid x-1\mid dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Show that $\int\limits_0^af(x)g(x)dx=2\int\limits_0^af(x)dx,$ if \(f\) and \(g\) are defined as \(f(x) = f(a - x)\) and \(g(x) + g(a - x)=4\)

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer in the value of $\int\limits_0^\frac{\pi}{2}log\bigg(\frac{\large 4+3\sin x}{\large 4+3\cos x}\bigg)dx$ is

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\int\frac{x^3}{\sqrt{1-x^8}} \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\cos^3x\;e^{log\sin x}dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int e^{3\log x}(x^4+1)^{-1}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int f'(ax+b)[f(ax+b)]^n\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^1x\;e^x\;dx=1\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_{-1}^1x^{17}\cos^4x\;dx=0\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^\frac{\pi}{2}\sin^3x\;dx=\frac{2}{3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in $\int\frac{dx}{e^x+e^{-x}}$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in $\int\frac{\large \cos 2x}{\large (\sin x+\cos x)^2}dx$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=e^x+1\qquad:\;y''-y'=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x^2+2x+C\qquad:\;y'-2x-2=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\cos x+C\qquad:y'+\sin x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation\[y=\sqrt{1+x^2}\qquad:\;y'\;=\frac{xy}{1+x^2}\]

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x\sin x\qquad:xy'=y+x\sqrt{x^2-y^2} (x\neq0\;and\;x>y\;or\;x<-y)$

asked Nov 30, 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

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the general solution of a differential equation of fourth order are

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the particular solution of a differential equation of third order are

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles touching the \(y\) - axis at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Which of the following differential equations has $y = x$ as one of its particular solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx} $$=\sqrt {4-y^2} \; (-2\lt y \lt 2) $

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

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

Find the general solution $x^5\large\frac{dy}{dx}$$=-y^5$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $e^x\tan y\;dx+(1-e^x)\sec ^2y\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}=$$y\tan x;\;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve,the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]

asked Nov 29, 2012 by sreemathi.v

1 answer

A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution

asked Nov 29, 2012 by sreemathi.v

1 answer

Which of the following is a homogeneous differential equation?

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$

asked Nov 29, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 $ is

asked Nov 29, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $(1-y^2)\large\frac{dx}{dy}$$+yx=ay\: \;is$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the vector and the cartesian equations of the line that passes through the points $(3, -2, -5), (3, -2, 6).$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the vector and the cartesian equations of the lines that passes through the origin and $(5, -2, 3).$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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