Recent questions tagged sec-1

Evaluate the following problems using properties of integration: $\int\limits_{0}^{\large\frac{\pi}{2}}\sin^{3}x\cos xdx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{-\pi}{4}}^{\large\frac{\pi}{4}}x^{3}\cos^{3} xdx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{-1}^{1}\sin x\cos^{4} x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{2}} e^{3x}\cos x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{1} x^{2} e^{x} dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{2}}\sin 2x \cos x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{1}\large\frac{(\sin^{-1}x)^{3}}{\sqrt{1-x^{2}}}$$dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{1}^{2}\large\frac{dx}{x^{2}+5x+6}$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\pi/2}\large\frac{\sin x dx}{9+\cos^{2}x}$

asked Apr 27, 2013 by poojasapani_1

0 answers

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\pi/2}\large(\frac{\sin^{-1}x^{3}}{\sqrt{1-x^{2}}})$$dx$

asked Apr 26, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{4}}2\sin^{2}x \sin 2x dx$

asked Apr 26, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{1}\sqrt{9-4x^{2}}dx$

asked Apr 26, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{2}}\cos^{3}x dx$

asked Apr 26, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\pi/2}\sin^{2}xdx$

asked Apr 26, 2013 by poojasapani_1

1 answer

Using Euler's theorem prove the following: if$\;V=x^{ax+by}$ and $\;z$ is a homogenous function of degree $\;n$ in $\;x$ and $\;y$ prove that $\;x=\large\frac{\partial v}{\partial x}$+$y\large\frac{\partial v}{\partial y}$=$(ax+by+n)V.$

asked Apr 26, 2013 by poojasapani_1

0 answers

Using Euler's theorem prove the following: if $u$ is a homogenous function of $x$ and $y$ of degree$\;n$, prove that$\;x\large\frac{\partial^{2} u}{\partial x^{2}}$+$y\large\frac{\partial^{2}u}{\partial x\partial y}$=$(n-1)\large\frac{\partial u}{\partial x}$

asked Apr 26, 2013 by poojasapani_1

0 answers

Using Euler's theorem prove the following: $\;u=xy^{2}\sin\large(\frac{x}{y}),$ show that $x\large\frac{\partial u}{\partial x}+$$y=\large\frac{\partial u}{\partial y}=$$3u.$

asked Apr 26, 2013 by poojasapani_1

1 answer

Using Euler's theorem prove the following: if$\;u=\tan^{-1}\large[\frac{x^{3}+y^{3}}{x-y}]$ prove that $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}=$$\sin 2u$

asked Apr 26, 2013 by poojasapani_1

1 answer

Find $\large\frac{\partial w}{\partial u}$ and $\large\frac{\partial w}{\partial v}$ if $\;w=\sin^{-1}xy$ where $x=u+v,y=u-v$

asked Apr 26, 2013 by poojasapani_1

1 answer

Find $\large\frac{\partial w}{\partial r}$ and $\large\frac{\partial w}{\partial \theta}$ if $\;w=\log(x^{2}+y^{2})$where $\;x=r\cos\theta,y=r\sin\theta$

asked Apr 26, 2013 by poojasapani_1

1 answer

Using chain rule find $ \large\frac{dw}{dt}$ for each of the following$\;w=xy+z$ where $x=\cos t,y=\sin t $

asked Apr 25, 2013 by poojasapani_1

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following:$\;w=\large(\frac{x}{x^{2}+y^{2}})$ where $x=\cos t,y=\sin t.$

asked Apr 25, 2013 by poojasapani_1

1 answer

If$\;u=e^{y}\sin y\frac{x}{y}+e^{y}\cos x \frac{y}{x},$ Show that $x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=o$

asked Apr 25, 2013 by poojasapani_1

0 answers

Using chain rule find $\large\frac{dw}{dt}$ for each of the following :$w=\log(x^{2}+y^{2})$ where $x=e^{t},y=e^{-t}$

asked Apr 25, 2013 by poojasapani_1

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following : $w=e^{xy}$ Where $x=t^{2},y=t^{3}$

asked Apr 25, 2013 by poojasapani_1

1 answer

If $u= e^{\large\frac{x}{y}}\sin\frac{x}{y}+e^{\large\frac{y}{x}}\cos\frac{y}{x},$ Show that $ x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

asked Apr 25, 2013 by poojasapani_1

1 answer

If $u=\sqrt{x^{2}+y^{2}},$ Show that $ x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

asked Apr 25, 2013 by poojasapani_1

1 answer

Varify $\large\frac{\partial^{2} y}{\partial x\partial y}=\frac{\partial^{2} y}{\partial y\partial x}$ for the following function;$\;u=\tan^{-1}\large(\frac{x}{y})$

asked Apr 25, 2013 by poojasapani_1

1 answer

Verify $\large\frac{\partial ^{2} y}{\partial x\partial y}=\frac{\partial ^{2} y}{\partial y\partial x}$ for the following function;$\;u=\sin 3x\cos4y$

asked Apr 25, 2013 by poojasapani_1

1 answer