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Answers posted by sreemathi.v

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Find the integrals of the functions\[\sin^4x\]
answered Jan 30, 2013
Toolbox: $(i)1-\sin^2x=\cos^2x.$ $(ii)\int\cos xdx=\sin x+c.$ $(iii)\sin^2x=\f...
0 votes
Find the integrals of the functions $\frac{\cos x}{1+\cos x}$
answered Jan 30, 2013
Toolbox: $1+\cos x=2cos^2\frac{x}{2}.$ $\cos x=2\cos^2\frac{x}{2}-1.$ $\int\se...
0 votes
Find the integrals of the functions $\frac{1-\cos x}{1+\cos x}$
answered Jan 30, 2013
Toolbox: (i)$1-\cos x=2\sin^2\frac{x}{2}$. (ii)$1+\cos x=2\cos^2\frac{x}{2}$. ...
0 votes
Find the integrals of the functions\[\sin4x\;\sin8x\]
answered Jan 30, 2013
Toolbox: (i)$2\sin x\sin y=\cos(A-B)-\cos(A+B).$ $(ii)\int\sin xdx=-\cos x+c.$ ...
0 votes
Find the integrals of the functions $\sin x\;\sin2x\;\sin3x$
answered Jan 30, 2013
Toolbox: (i)$\sin x.\sin y=\cos(x-y)-\cos (2x+3y).$ (ii)$2\sin x\cos y=\sin(x+y)+\si...
0 votes
Find the integrals of the functions\[\sin^3x\;\cos^3x\]
answered Jan 30, 2013
Toolbox: (i)$\sin^2x=1-\cos^2x.$ (ii)$\int x^ndx=\begin{bmatrix}x^{n+1}{n+1}\end{bma...
0 votes
Find the integrals of the functions\[\sin^3(2x+1)\]
answered Jan 30, 2013
Toolbox: (i)$\sin^2x=\frac{1-\cos 2x}{2}$ (ii)$\sin^3x=\frac{3\sin x-\sin 3x}{4}$ ...
0 votes
Find the integrals of the functions\[\cos2x\;\cos4x\;\cos6x\]
answered Jan 30, 2013
Toolbox: $(i)2\cos x\cos y=\cos (x+y)+\cos (x-y).$ $(ii)\frac{1+\cos 2x}{2}=\cos^2x....
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Choose the correct answer in $\Large \int \normalsize\frac{dx}{\sin^2x\cos^2x}$ equals
answered Jan 30, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Choose the correct answer in $\Large \int \normalsize \frac{10x^9+10^xlog_{e^{10}}dx}{x^{10}+{10}^x}$ equals
answered Jan 30, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{x^3\sin\bigg(\tan^{-1}x^4\bigg)}{1+x^8}$
answered Jan 30, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{(x+1)(x+log\: x)^2}{x}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{(1+log\: x)^2}{x}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{\sqrt{\tan x}}{\sin x\cos x}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{1}{1-\ tanx}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form by changin...
0 votes
Integrate the function $\frac{1}{1+\cot x}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\sin x}{(1+\cos x)^2}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\sin x}{1+\cos x}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function\[\cot x\;log \sin x\]
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function\[\frac{\cos x}{\sqrt{1+\sin x}}\]
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function\[\sqrt{\sin2x}\cos2x\]
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function$\frac{\cos\sqrt x}{\sqrt x}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\int \frac{1}{\cos^2x(1-\tan x)^2}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function: $\int \frac{\large 2cos\: x-3sin\: x}{\large 6cos\: x+4sin\: x}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{\large \sin^{-1}x}{\large \sqrt{1-x^2}}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\sec^2(7-4x)$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\tan^2(2x-3)$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{\large e^{2x}-e^{-2x}}{\large e^{2x}+e^{-2x}}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\frac{\large e^{2x}-1}{\large e^{2x}+1}$
answered Jan 29, 2013
Toolbox: (i)Method of substitution : Given f(x)dx can be transformed into another fo...
0 votes
Integrate the function $\Large \frac{\large e^{\tan^{-1}x}}{\large 1+x^2}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\large x}{\large e^{x^2}}$
answered Jan 29, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $e^{2x+3}$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\large x}{\large 9-4x^2}$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\large 1}{\large x(log x)^m},x\;>\;0$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\large x^2}{(\large 2+3x^3)^3}$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $(x^3-1)^\frac{1}{3}\;x^5$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form by changin...
0 votes
Integrate the function $\frac{\large x}{\large \sqrt{x+4}},x\;>\;0$
answered Jan 28, 2013
Toolbox: Method of substitution : Given f(x)dx can be transformed into another form ...
0 votes
Integrate the function $\frac{\large 1}{\large x-\sqrt x}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $(4x+2)\sqrt{x^2+x+1}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $x\;\sqrt{1+2x^2}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $x\;\sqrt{x+2}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $\sqrt{ax+b}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $\sin(ax+b)\;\cos(ax+b)$
answered Jan 28, 2013
Toolbox: (i)Method of substitution: Given $\int f(x)dx$ can be transformed into anot...
0 votes
Integrate the function $\sin x\sin(\cos x)$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function $\frac{\large 1}{\large x+x\;log x}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function$\frac{(\large log \; x)^2}{\large x}$
answered Jan 28, 2013
Toolbox: Method of substitution: Given $\int f(x)dx$ can be transformed into another...
0 votes
Integrate the function$\frac{\large 2x}{\large 1+x^2}$
answered Jan 28, 2013
Toolbox: $(i)\;Method \;of \;substitution:$ Given $\int f(x)dx$ can be transformed i...
0 votes
If $\frac{\large d}{\large dx}f(x)=4x^3-\frac{\large 3}{\large x^4}$ such that $f(2)=0$.Then $f(x)$ is
answered Jan 28, 2013
Toolbox: $\frac{d}{dx}[F(x)+c]=f(x)$. Given $\frac{d}{dx}f(x)=4x^3-\frac{3}{x^4}.$...
0 votes
The anti derivative of $\bigg(\sqrt x+\frac{1}{\sqrt x}\bigg)$ equals
answered Jan 28, 2013
Toolbox: $(i)\;\int x^n=\frac{x^n+1}{n+1}+c.$ $(ii)\;\frac{d}{dx}[f(x)+c]=f(x)$. ...
0 votes
Find the integral $\displaystyle\int\frac{\large 2-3\sin x}{\large \cos^2x}dx$
answered Jan 27, 2013
Toolbox: $(i)\;\int sin xdx=-\cos x$. $(ii)\;\int\sec^2xdx=\tan x.$ $\int\fr...
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