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Recent questions tagged easy

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

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area enclosed by the parabola \(4y = 3x^2\) and the line \(2y = 3x + 12.\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the smaller region bounded by the ellipse \( \frac{\large x^2}{\large 9} + \frac{\large y^2}{\large 4} =1\) and the line \( \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

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 \( -x -y = 1\)].

asked Dec 4, 2012 by thanvigandhi_1

1 answer

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

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the area bounded by the curve $ y = x^3$, the $x$ - axis and the ordinates $x = -2$ and $x = 1$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function\[\sqrt{4-x^2}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function\[\sqrt{1-4x^2}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function\[\sqrt{1+\frac{x^2}{9}}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize \sqrt{1+x^2}dx$ is equal to \[\begin{array}{l}(A)\;\frac{x}{2}\sqrt{1+x^2}+\frac{1}{2}log\LARGE\mid\normalsize\bigg(x+\sqrt{1+x^2}\bigg)\LARGE\mid\normalsize+C \\(B)\;\frac{2}{3}(1+x^2)^\frac{3}{2}+C\qquad \\ (C)\;\frac{2}{3}x(1+x^2)^\frac{3}{2}+ C \\ (D)\;\frac{x^2}{2}\sqrt{1+x^2}+\frac{1}{2}x^2log\LARGE\mid\normalsize x+\sqrt{1+x^2}\LARGE\mid\normalsize+C \end{array}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in $ \Large \int \normalsize \sqrt{x^2-8x+7} \: dx$ is equal to\[ \begin{array}{l} (A)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}+9\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \\ (B)\frac{1}{2}(x+4)\sqrt{x^2-8x+7}+9\;log\mid x+4+\sqrt{x^2-8x+7}\mid + \; C \\ (C) \frac{1}{2}(x-4)\sqrt{x^2-8x+7}-3\sqrt2log\mid x-4+\sqrt{x^2-8x+7}\mid+ \; C \\ (D)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}-\frac{9}{2}\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \end{array}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums\[\int\limits_{-1}^1e^xdx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_{-1}^1(x+1)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_2^3\frac{1}{x}dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_1^2(4x^3-5x^2+6x+9)\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\sin 2x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 2}\cos 2x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in the area of the region bounded by the curve $y^2 = 4x,\; y$ - axis and the line $y = 3$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral\[\int\limits_4^5e^x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\tan x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in area lying in the first quadrant and bounded by the circle $x^2 + y^2 = 4 $ and the lines $x = 0$ and $x = 2$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral\[\int\limits_\frac{\Large \pi}{\Large 6}^\frac{\Large \pi}{\Large 4}cosec x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral\[\int\limits_0^1\frac{dx}{\sqrt{1-x^2}}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^1\frac{dx}{1+x^2}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_2^3\frac{dx}{x^2-1}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^1x\;e^{x^2}dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\large\pi}{4}(2\sec^2x+x^3+2)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral $\int\limits_0^\pi(\sin^2\frac{x}{2}-\cos^2\frac{x}{2})dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

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

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in $\int\limits_1^\sqrt 3\frac{dx}{1+x^2}\;equals$\[(A)\;\frac{\pi}{3}\qquad(B)\;\frac{2\pi}{3}\qquad(C)\;\frac{\pi}{6}\qquad(D)\;\frac{\pi}{12}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the smaller part of the circle $x^2 + y^2 = a^2$ cut off by the line $x =\Large { \frac{a}{\sqrt 2}}$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region bounded by $y^2 = 9x,\; x = 2,\; x = 4$ and the $x$ - axis in the first quadrant.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x$ - axis.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in $\int\limits_0^\frac{2}{3}\frac{dx}{4+9x^2}$ equals

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution\[\int\limits_0^1\frac{x}{x^2+1}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution\[\int\limits_0^\frac{\large \pi}{2}\frac{\sin x}{1+\cos^2x}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution\[\int\limits_{-1}^1\frac{dx}{x^2+2x+5}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the integral using substitution $\displaystyle\int\limits_1^2\bigg(\frac{1}{x}-\frac{1}{2x^2}\bigg)e^{2x}dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer If f(x)=$\int\limits_0^x t\sin t\;dt,$ then f'(x) is

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^\frac{\Large \pi}{\Large 2}\cos^2x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\Large \pi}{\Large 2}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\sin^\frac{3}{2}\;x\;dx}{\sin^\frac{3}{2}\;x+\cos^\frac{3}{2}\;x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\cos^5x\;dx}{\sin^5x+\cos^5x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^1x\;(1-x)^n\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^2x\sqrt{2-x}dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^2\;x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^7\;x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^{2\pi}\cos^5x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

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