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Recent questions tagged difficult

Integrate the rational functions\[\frac{x^3+x+1}{x^2-1}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{2}{(1-x)(1+x^2)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{1}{x^4-1}$

asked Dec 5, 2012 by sreemathi.v

1 answer

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let \(\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k \) . Find a vector \( \overrightarrow d\) which is perpendicular to both \(\overrightarrow a\) and \(\overrightarrow b\) , and \( \overrightarrow c ⋅ \overrightarrow d =15\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If \( \overrightarrow a, \overrightarrow b, \overrightarrow c, \) are mutually perpendicular vectors of equal magnitudes, show that the vector \( \overrightarrow a + \overrightarrow b + \overrightarrow c\) is equally inclined to \( \overrightarrow a, \overrightarrow b and \overrightarrow c\).

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the rational functions\[\frac{1}{x(x^n+1)}\] \[Hint:multiply\;numerator\;and\;denominator\;by\;x^{n-1}and\;put\;x^n=t\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{(x^2+1)(x^2+2)}{(x^2+3)(x^2+4)}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{2x}{(x^2+1)(x^2+3)}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{1}{x(x^4-1)}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{1}{(e^x-1)} [Hint:Put\;e^x=\;t]$

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize\frac{\large dx}{\large x(x^2+1)}$equals

asked Dec 4, 2012 by sreemathi.v

1 answer

Using mathematical induction prove that \( \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} \) for all positive integers \(n\).

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $(\sin^{-1}x)^2$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function $\;\int\;e^{2x}\sin\; x$

asked Dec 4, 2012 by sreemathi.v

1 answer

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

asked Dec 4, 2012 by thanvigandhi_1

2 answers

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

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the the area bounded by the \(y\) - axis, \(y = \cos\: x\) and \(y = \sin\: x\) when \(0 \leq x \leq \frac{\large \pi}{2}\) is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral $\displaystyle\int\limits_1^2\frac{5x^2}{x^2+4x+3}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution $\begin{align}\int\limits_0^1\sin^{-1}\bigg(\frac{2x}{1+x^2}\bigg)dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer in the value of the integral$\begin{align}\int\limits_\frac{1}{3}^1\frac{(x-x^3)^\frac{1}{3}}{x^4}dx \end{align}$ is

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\pi\; log(1+\cos x)\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{5x}{(x+1)(x^2+9)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{\cos(x+a)\cos(x+b)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{(x^2+1)(x^2+4)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\large\frac{1}{\sqrt{\sin^3x\sin(x+\alpha)}}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{\sin^{-1}\sqrt x-\cos^{-1}\sqrt x}{\sin^{-1}\sqrt x+\cos^{-1}\sqrt x},$$x\;\in\;[0,1]$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\sqrt{\frac{1-\sqrt x}{1+\sqrt x}}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{\sqrt{x^2+1}[log(x^2+1)-2logx]}{x^4}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{2}\frac{\cos^2xdx}{\cos^2x+4\sin^2x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_\frac{\pi}{6}^\frac{\pi}{3}\frac{\sin x+\cos x}{\sqrt{\sin2x}}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^1\frac{dx}{\sqrt{1+x}-\sqrt x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{4}\frac{\sin x+\cos x}{9+16\sin 2x}\;dx\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{2}\sin 2x\tan^{-1}(sin x)\;dx\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals $\int\limits_0^{\pi}\large\frac{x\tan x}{\sec x+\tan x}$$\;dx$

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals: $\int\limits_1^4 [\; |x-1|+|x-2|+|x-3|\;]dx$

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_1^3\frac{dx}{x^2(x+1)}=\frac{2}{3}+log\frac{2}{3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate $ \large \int\limits_0^1e^{2-3x}\;$$dx\;$ as a limit of a sum

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}\qquad[Hint:\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}=\frac{1}{x^\frac{1}{3}\bigg(1+x^\frac{1}{6}\bigg)},put\;x=t^6]\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x-x^3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the direction cosines of the sides of the triangle whose vertices are (3, 5, -4), (-1, 1, 2) and ( -5, -5, -2).

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that if a plane has the intercepts $a, b, c$ and is at a distance of $p$ units from the origin, then $\large\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} = \frac{1}{p^2}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a, b and c are real numbers, and $\Delta = \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c\\ a+b & b+c & c+a \end{vmatrix}=0, $ show that either $a+b+c=0$ or $a=b=c.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 2 &-3 & 5\\ 3& 2 & -4\\ 1& 1& -2 \end{bmatrix}$, $\;$ find $A^{-1}.\;$ Using $ A^{-1}$ solve the system of equations: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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