Answers posted by sreemathi.v

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Find the integral $\int\sec x(\sec x+\tan x)dx$

answered Jan 27, 2013

Toolbox: $(i)\;\int sec^2xdx=\tan x+c$. $(ii)\;\int sec x\tan xdx=sec x+c$. ...

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Find the integral $\int(2x^2-3sin\: x+5\sqrt x)\;dx$

answered Jan 27, 2013

Toolbox: $(i)\;\int x^ndx=\frac{x^{n+1}}{n+1}+c$. $(ii)\;\int \sin xdx=-\cos x+c.$ ...

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Find the integral $\int\sqrt x\;(3x^2+2x+3)\;dx$

answered Jan 27, 2013

Toolbox: $(i)\int x^n dx=\frac{x^{n+1}}{n+1}+c$. $\int\sqrt x(3x^2+2x+3)dx.$ &...

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Find the integral $\int(1-x)\sqrt x\;dx$

answered Jan 27, 2013

Toolbox: $(i)\int x^n dx=\frac{x^{n+1}}{n+1}+c$. $\int(1-x)\sqrt xdx.$ ...

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Find the integral $\int\frac{\large x^3+3x+4}{\large \sqrt x}\;dx$

answered Jan 27, 2013

Toolbox: $\int x^n dx=\frac{x^{n+1}}{n+1}+c\;$ $\int\frac{x^3+3x+4}{\sqrt x}dx.$ We can split...

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Find an anti derivative(or integral)of the function by the method of inspection $\sin2x-4e^{3x}$

answered Jan 25, 2013

Toolbox: $\frac{d}{dx}[F(x)+c]=f(x),$ $\int f(x)\;dx=F(x)+c$ We know that $\...

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Find an anti derivative(or integral)of the function by the method of inspection $(ax+b)^2$

answered Jan 25, 2013

Toolbox: $\frac{d}{dx}[F(x)+c]=f(x),$ $\int f(x)\;dx=F(x)+c$ We know that $\...

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Find an anti derivative(or integral)of the function by the method of inspection $e^{2x}$

answered Jan 25, 2013

Toolbox: $\frac{d}{dx}[F(x)+c]=f(x),$ $\int f(x)\;dx=F(x)+c$ We know that $\...

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Find an anti derivative(or integral)of the function by the method of inspection $\cos 3x$

answered Jan 25, 2013

Toolbox: $\frac{d}{dx}[F(x)+c]=f(x),$ $\int f(x)\;dx=F(x)+c$ We know that $\...

0 votes

Find an anti derivative(or integral)of the function by the method of inspection $\sin 2x$

answered Jan 25, 2013

Toolbox: $\frac{d}{dx}[F(x)+c]=f(x),x\in I$ $\int f(x)\;dx=F(x)+c$ We know t...

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Using integration find the area of region bounded by the triangle whose vertices are $(-1, 0), (1, 3) $ and $(3, 2)$.

answered Jan 25, 2013

Toolbox: Equation of a line when two points are given is\[\frac{y-y_1}{y_2-y_1}=\frac{x-x_...

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Find the area of the region bounded by the parabola $y = x^2$ and $y = \left | x \right | $.

answered Jan 24, 2013

Toolbox: Whenever a function is represented by y=|x|,two cases arise: (i) y=x if $x\...

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The area between $x = y^2$ and $x = 4$ is divided into two equal parts by the line $x = a$, find the value of $a$.

answered Jan 24, 2013

Toolbox: whenever the area bounded by a curve and a line is divided into two equal parts,t...

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Find the area of the region bounded by $x^2 = 4y, y = 2, y = 4$ and the $y$ - axis in the first quadrant.

answered Jan 24, 2013

Toolbox: The area A of the region bounded by the curve x=g(y),y-axis and the lines y=c,y=d is giv...

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Choose the correct answer in the the area of the circle $x^2 + y^2 = 16$ exterior to the parabola $y^2 = 6x$ is \[\begin{array} (A) \frac{4}{3} (4\pi - \sqrt 3) \quad &(B) \frac{4}{3} (4\pi + \sqrt 3) \quad & (C) \frac{4}{3} (8\pi - \sqrt 3) \quad & (D) \frac{4}{3} (8\pi + \sqrt 3) \end{array}\]

answered Jan 23, 2013

Toolbox: Suppose we are given two curves represented by y=f(x),y=g(x) where $f(x)\geq g(x)...

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Choose the correct answer in the the area bounded by the curve $y = x |\; x\; | ,\; x$ - axis and the ordinates $x = -1$ and $x = 1$ is given by [Hint : $y = x^2$ if $x > 0$ and $y = -x^2$ if $x < 0$].

answered Jan 23, 2013

Toolbox: Whenever a function is represented by y=|x| two cases arises. (i) y=x if $x...

0 votes

Find the area of the region ${(x, y) : y^2\: \leq \: 4x, 4x^2 + 4y^2\: \leq\: 9}$

answered Jan 23, 2013

Toolbox: Suppose we are given two curves represented by f(x),y=g(x) where $f(x)\geq g(x)$ in [a,b...

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Find the area bounded by curves {(x, y)$ : y\: \geq\: x^2\: and \: y = |\; x\; |$}.

answered Jan 22, 2013

Suppose we are given two curves represented by y=f(x),y=g(x) where $f(x)\geq g(x)$ in [a,b] the...

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Using the method of integration find the area bounded by the curve I x I + I y I =1 . [Hint: The required region is bounded by lines $x + y = 1, x - y = 1, -x + y = 1$ and $ -x -y = 1$].

answered Jan 22, 2013

Whenever a function is represented by y=|x| there arises two cases. (i)y=x if $x\geq 0$ ...

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

answered Jan 22, 2013

Suppose we are given two curves represented by y=f(x) and y=g(x), where $f(x)\geq g(x)$ in [a,b...

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Find the area enclosed between the parabola $y^2 = 4ax$ and the line $y = mx.$

answered Jan 21, 2013

Suppose we are given two curves represented by y=f(x);y=g(x) where $f(x)\geq g(x)$ in [a,b] ...

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sketch the graph of y=|x+3| and evaluate $\int_{-6}^0|x+3| dx.$

answered Jan 21, 2013

y=|x+3| can have two possibilities $\;\;(i)\;y=x$ where $x\geq 0$ $\;\;(ii)\;\;y=-x$ wh...

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Find the area between the curves $y = x$ and $y = x^2.$

answered Jan 21, 2013

Suppose we are given two curves represented by y=f(x),y=g(x) where $f(x)\geq g(x)$ in [a,b]. ...

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