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Recent questions tagged short-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

Using integration,find the area of the region bounded by the line $2y=5x+7,x$-axis and the lines $x=2$ and $x=8.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Calculate the area under the curve $y=2\sqrt x$ included between the lines $x=0$ and $x=1$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Sketch the region $\{(x,0):y=\sqrt {4-x^2}$} and $x$-axis.Find the area of the region using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the line $x=2$ and the parabola $y^2=8x$.

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 curve $y^2=4x,x^2=4y$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y=x^3$ and $y=x+6$ and $x=0$.

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

Evaluate the following:$\int\limits_1^2\frac{dx}{\sqrt{(x-1)(2-x)}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^{\Large \frac{\pi}{2}}\Large \frac{\tan xdx}{1+m^2\tan^2x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1\frac{dx}{e^x+e^{-x}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following as limits of sums: $ \int\limits_0^2e^xdx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following as limits of sums: $\int\limits_0^2(x^2+3)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\displaystyle\int\frac{dx}{x\sqrt{x^4-1}}\;(Hint:Put\;x^2=\sec\theta)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\displaystyle\int\frac{\cos x-\cos 2x}{1-\cos x}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following : $\begin{align} \int \frac{\sin^6x+\cos^6x}{\sin^2x \cos^2x}dx \end{align}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following\[\int\frac{(\cos 5x+\cos 4x)}{1-2\cos 3x}dx\]

asked Jan 14, 2013 by sreemathi.v

0 answers

Evaluate the following $\int\frac{\sin^{-1}x}{(1-x^2)^{\frac{3}{2}}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt {2ax-x^2}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following\[\int\frac{x^2}{1-x^4}dx\;put\;x^2=t\]

asked Jan 14, 2013 by sreemathi.v

0 answers

Evaluate the following $\int\frac{3x-1}{\sqrt{x^2+9}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{dt}{\sqrt {3t-2t^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\displaystyle\int\frac{dx}{\sqrt {16-9x^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{\sqrt{1+ x^2}}{x^4}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\large\int\frac{ x^{\frac{1}{2}}}{1+x^{\frac{3}{4}}}dx$ $(Hint:Put\;x=z^4)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt{\frac{a+x}{a-x}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\displaystyle\int \large \frac{( x)}{\sqrt x+1}$$dx \quad(Hint:Put\;\sqrt x=z)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt{1+\sin x}\;dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{(\sin x+\cos x)}{\sqrt {1+\sin 2x}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\tan^2 x\sec^4 x\;dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following$\int\frac{dx}{1+\cos x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\large\int\frac{(1+\cos x)}{x+\sin x}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following$\displaystyle\int\frac{e^{6log x}-e^{5log x}}{e^{4log x}-e^{3log x}}$$dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $ \displaystyle\int\frac{(x^2+2)}{x+1}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Verify the following $ \large\int\frac{2x+3}{x^2+3x}dx=log \mid x^2+3x\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

Prove that $f(x)=\sin x+\sqrt 3\cos x$ has maximum value at $x=\Large\frac{1}{6}$.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that for a$\quad 1,f(x)=\sqrt 3\sin x-\cos x-2ax+b$ is decreasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=2x+\cot^{-1}x+log\bigg(\sqrt {(1+x^2)}-x\bigg)$ is increasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that the line $\Large \frac{x}{a}+\frac{y}{b}\normalsize=1$,touches the curve $y=b.e^{\Large \frac{-x}{a}}$ at the point where the curve intersects the axis of y.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what points on the curve $x^2+y^2-2x+4y+1=0$,the tangents are parallel to the y-axis?

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line x+3y=4.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the angle of intersection of the curves $y=4-x^2$ and $y=x^2$.

asked Jan 11, 2013 by sreemathi.v

1 answer

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