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1 votes
1 answer
31
ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is $1/4$ $1/6$ $1/8$ $1/24$
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$$f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$$Then the area enclosed between the graphs of...
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33
How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
$$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$$
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34
Ace Test Series: Calculus - Integration
Can anyone help me with solving this type of problem? I want some resource from where I can learn to solve this type on integration, as according to solution it is a function of α, so I did not understand the solution.
Can anyone help me with solving this type of problem? I want some resource from where I can learn to solve this type on integration, as according to solution it is a func...
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35
#integration
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$
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36
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosx-cos5x)/10 2.(5sinx-sin5x)/10 3.both 4.none
$I=\int sin(2x) cos(3x) dx$1.(5cosx-cos5x)/102.(5sinx-sin5x)/103.both4.none
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1 votes
0 answers
37
NIELIT 2018-16
The value of $\int_c \frac{2x^2-5}{(x+2)^2 (x^2+4)x^2}dx$, (where $c$ is the square with vertices $1+i, 2+i, 2+2i, i+2i$) is: $0$ $\pi i$ $2 \pi i$ $4 \pi i$
The value of $\int_c \frac{2x^2-5}{(x+2)^2 (x^2+4)x^2}dx$, (where $c$ is the square with vertices $1+i, 2+i, 2+2i, i+2i$) is:$0$$\pi i$$2 \pi i$$4 \pi i$
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1 votes
1 answer
38
NIELIT 2018-29
Using Green’s theorem in plane, evaluate $\int_c (2x-y) dx + (x+y)dy$, where $c$ is the circle $x^2+y^2=4$ in the plane: $2 \pi$ $4 \pi$ $-4 \pi$ $8 \pi$
Using Green’s theorem in plane, evaluate $\int_c (2x-y) dx + (x+y)dy$, where $c$ is the circle $x^2+y^2=4$ in the plane:$2 \pi$$4 \pi$$-4 \pi$$8 \pi$
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39
Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$
$\int_{1}^{∞}\frac{dx}{x^6+1}$
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2 votes
1 answer
40
Calculus-Integration
$\int x^7.e^{x^4}dx$ How to do this?
$\int x^7.e^{x^4}dx$How to do this?
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0 votes
1 answer
41
Integration
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
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0 votes
1 answer
42
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
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0 votes
1 answer
43
Gilbert Strang
Differentiate y=$x^{-1/lnx}$
Differentiatey=$x^{-1/lnx}$
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0 votes
0 answers
44
Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$
$\int_{0}^{1}(x^2+1)^4dx$
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0 votes
1 answer
45
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
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1 votes
1 answer
46
Calculus-Definite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$
What is the value of $\int_0^\pi log(1+cosx)dx$
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0 votes
1 answer
47
Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
Solve$\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
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48
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?$0$$\sqrt{\pi}...
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0 votes
1 answer
49
Area between curves
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is . I am getting $128√2$.
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is .I am getting $128√2$.
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1 votes
1 answer
50
Definite Integral
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$ Please explain how to solve it.
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$Please explain how to solve it.
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0 votes
0 answers
51
Integration
$f\left ( x \right )=$\int_{-2}^{2}x^{-\frac{2}{7}}dx$ Is this function f(x) is continuous, bounded and differentiable? (In exam hall is it possible to draw the graph for this function f(x), or some other procedure to follow to ans this)
$f\left ( x \right )=$$\int_{-2}^{2}x^{-\frac{2}{7}}dx$Is this function f(x) is continuous, bounded and differentiable?(In exam hall is it possible to draw the graph for ...
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0 votes
0 answers
52
Integration
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
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53
Multiple integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
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0 votes
3 answers
54
Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
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55
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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0 votes
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56
Calculus Integration
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
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0 votes
1 answer
57
ISI-2014-07
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is $2\sqrt2\pi^2$ $\dfrac{\pi^2}{2\sqrt2}$ $\dfrac{\pi^2}{\sqrt2}$ $\sqrt2\pi^2$
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is$2\sqrt2\pi^2$$\dfrac{\pi^2}{2\sqrt2}$$\dfrac{\pi^2}{\sqrt2}$$\sqrt2\pi^2$
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0 votes
2 answers
58
ISI-2014-5
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$ $\text{is 0}$ $\text{is 1}$ $\text{is 2}$ $\text{does not exist}$
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$$\text{is 0}$$\text{is 1}$$\text{is 2}$$\text{does not exist}$
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28 votes
4 answers
60
GATE CSE 2018 | Question: 16
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
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