Recent questions tagged medium

The area of the region bounded by the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ is \begin{array}{1 1}(A)\;2 \pi sq.units & (B)\;20{\pi}^2 sq.units\\(C)\;16{\pi}^2 sq.units & (D)\;25\pi sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Using elementary transformation, find the inverse of the following matrix $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

The area of the region bounded by parabola $y^2=x$ and the straight line $2y=x$ is \begin{array}{1 1}(A)\;\frac{4}{3} sq.units & (B)\;1 sq.units\\(C)\;\frac{2}{3} sq.units & (D)\;\frac{1}{3}sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

The area of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is \begin{array}{1 1}(A)\;\frac{3}{8}sq.units & (B)\;\frac{5}{8}sq.units\\(C)\;\frac{7}{8}sq.units & (D)\;\frac{9}{8} sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Prove that : $ \cos^{-1}\large \frac{4}{5}+\tan^{-1}\large\frac{3}{5}$$=\tan^{-1}\large\frac{27}{11} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Draw a rough sketch of the given curve $y=1+|x+1|,x=-3,x=3,y=0$ and find the area of the region bounded by them,using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area bounded by the curve $y=2\cos x$ and the $x$-axis from $x=0$ to x=2$\pi$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Draw a rough sketch of the region {(x,y):$y^2\leq 6ax $ and $x^2+y^2\leq 16a^2$}.Also find the area of the region sketched using method of integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by $y=\sqrt x$ and $y=x.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Determine the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval [1,5].Find the area under the curve and between the lines $x=1$ and $x=5$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region enclosed by the parabola $x^2=y$ and the line $y=x+2$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region included between $y^2=9x$ and $y=x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the parabola $y^2=2px,x^2=2py.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curves $y^2=9x,y=3x.$

asked Jan 15, 2013 by sreemathi.v

1 answer

$\int\limits_0^{\Large\frac{\pi}{2}}\cos x\;e^{\sin x} dx$ is equal to ____________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x+\sin x}{1+\cos x}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;\log\mid1+\cos x\mid+C & (B)\;\log\mid x+\sin x\mid+C\\(C)\;x-\tan\frac{x}{2}+C & (D)\;x\;\tan\frac{x}{2}+C \end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^9}{(4x^2+1)^6}\normalsize dx $ is equal to\begin{array}{1 1}(A)\;\frac{1}{5x}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C & (B)\;\frac{1}{5}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C\\(C)\;\frac{1}{10x}(1+4)^{-5}+C & (D)\;\frac{1}{10}\bigg(\frac{1}{x^2}+4\bigg)^{-5}+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int e^x\bigg(\frac{1-x}{1+x^2}\bigg)^2 \normalsize dx$ is equal to

asked Jan 15, 2013 by sreemathi.v

1 answer