Recent questions tagged exemplar

Evaluate the following: $\int\limits_0^\pi x\sin x\cos^2xdx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1\frac{xdx}{\sqrt{1+x^2}}$

asked Jan 14, 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

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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

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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

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Evaluate the following $\int\frac{x}{x^4-1}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt {5-2x+x^2}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

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

Verify the following$ \int\frac{2x-1}{2x+1}dx=x-log \mid (2x+3)^2\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

The least value of the function $f(x)=ax+\frac{b}{x}(a>0,b>0,x>0)$ is ___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=\Large\frac{2x^2-1}{x^4}$,x>0,decreases in the interval__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The equation of normal to the curve y=tan x at (0,0) is___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point_________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of $\Large\frac{1}{x}$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

$f(x)=x^x$ has a stationary point at

asked Jan 12, 2013 by sreemathi.v

1 answer

Maximum slope of the curve $y=x^3+3x^2+9x-27$ is

asked Jan 12, 2013 by sreemathi.v

1 answer

At $x=\Large\frac{5}{6}$$,f(x)=2\sin 3x+3\cos 3x$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of sin x,cos x is

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=2x^3-3x^2-12x+4$,has

asked Jan 12, 2013 by sreemathi.v

1 answer

The smallest value of the polynomial $x^3-18x^2+96x$ in [0,9] is

asked Jan 11, 2013 by sreemathi.v

1 answer

If x is real,the minimum value of $x^2-8x+17$ is

asked Jan 11, 2013 by sreemathi.v

1 answer

The function f(x)+tan x-x

asked Jan 11, 2013 by sreemathi.v

1 answer

Which of the following functions is decreasing on $\bigg(0,\frac{1}{2}\bigg)$

asked Jan 11, 2013 by sreemathi.v

1 answer

The function $f(x)=4\sin^3x-6\sin^2x+12sin x+100$ is strictly

asked Jan 11, 2013 by sreemathi.v

1 answer

$y=x(x-3)^2$ decreases for the values of x given by:

asked Jan 11, 2013 by sreemathi.v

1 answer

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