Recent questions tagged medium

Find the area of the region in the first quadrant enclosed by $x$ - axis, line $x = \sqrt {3}\: y$ and the circle $x^2 + y^2 = 4$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 16} + \frac{\Large y^2}{\Large 9} = 1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region bounded by $x^2 = 4y, y = 2, y = 4$ and the $y$ - axis in the first quadrant.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution $\int\limits_0^\frac{\large\pi}{2}\sqrt{\sin\phi}\cos^5\phi\;d\phi$

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution $\int\limits_0^2 x\sqrt{x+2}\;(Put\;x+2=t^2)$

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution\[\int\limits_0^2\frac{dx}{x+4-x^2}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_{-5}^5\mid x+2 \mid\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_2^8\mid x-5 \mid\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $ \begin{align}\int\limits_0^\frac{\pi}{4} log (1+\tan x)\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals, evaluate the integral $\int\limits_0^\frac{\Large \pi}{\Large 2}(2 \log \sin x-\log \sin 2x)\;dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\pi\frac{x\;dx}{1+\sin x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer in the value of $\displaystyle\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}(x^3+x\cos x+\tan^5x+1)dx$ is

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

Integrate the function $\begin{align}\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}\end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\int\frac{\cos x}{\sqrt{4-\sin^2x}} \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{\sin^8x-\cos^8x}{1-2\sin^2x\cos^2x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{e^x}{(1+e^x)(2+e^x)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{2+\sin2x}{1+\cos2x}$$e^x$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{x^2+x+1}{(x+1)^2(x+2)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\tan^{-1}\sqrt{\frac{1-x}{1+x}}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_\frac{\pi}{2}^\pi e^x\bigg(\frac{1-\sin x}{1-\cos x}\bigg)dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{4}\frac{\sin x\cos x}{\cos^4x+\sin^4x}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^\frac{\pi}{4}2\tan^3x\;dx=1-log2\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^1\sin^{-1}x\;dx=\frac{\pi}{2}-1\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers if $f(a+b-x) = f(x)$ , then $\int\limits_a^bx\;f(x)dx$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in the value of $\int\limits_0^1\tan^{-1}\bigg(\frac{\large 2x-1}{\large 1+x-x^2}\bigg)dx\;is$\[(A)\;1\qquad(B)\;0\qquad(C)\;-1\qquad(D)\;\frac{\pi}{4}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x^2(x^4+1)^\frac{3}{4}}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x\sqrt{ax-x^2}}[Hint:Put\;x=\frac{a}{t}]\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{\sqrt{x+a}+\sqrt{x+b}}\]

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 $y-\cos y=x\qquad:\;(y\sin y+\cos y+x)y'=y$

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

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. $y=a\: e^{3x}+b\: e^{-2x}$

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 $y=e^{2x}(a+bx)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(x^3+x^2+x+1)\large\frac{dy}{dx}$$=2x^2+x;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $x(x^2-1)\large\frac{dy}{dx}$$=1;y=0\;when\;x=2$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y'=e^x\;\sin x.$

asked Nov 30, 2012 by sreemathi.v

1 answer

For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $(x^2+xy)\;dy=(x^2+y^2)\;dx$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\;dy-y\;dx=\sqrt{x^2+y^2}dx$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

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