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Recent questions tagged integration

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Best Open Video Playlist for Integration Topic | Calculus
Please list out the best free available video playlist for Integration Topic from Calculus as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video lists. You can add ... but standard ones are more likely to be selected as best. For the full list of selected videos please see here

makhdoom ghaya asked in Study Resources Aug 15

by makhdoom ghaya

18 views

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2

math book
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find

amit166 asked in Calculus Sep 25, 2021

165 views

0 votes

1 answer

3

#mathematics
What is the difference between Integration and Summation? Which one produces a greater value in the same range?

Crackca asked in Calculus Sep 14, 2021

117 views

0 votes

1 answer

4

NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$

Lakshman Patel RJIT asked in Calculus Mar 31, 2020

by Lakshman Patel RJIT

341 views

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2 answers

5

NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$

Lakshman Patel RJIT asked in Calculus Mar 31, 2020

by Lakshman Patel RJIT

331 views

2 votes

1 answer

6

ISI2014-DCG-12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these

Arjun asked in Calculus Sep 23, 2019

by Arjun

469 views

3 votes

1 answer

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ISI2014-DCG-31
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$

Arjun asked in Calculus Sep 23, 2019

by Arjun

307 views

1 vote

1 answer

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ISI2014-DCG-47
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is $\frac{\pi}{6} + \sqrt{3}$ $\frac{\pi}{6} - \sqrt{3}$ $0$ $\frac{1}{2}$

Arjun asked in Calculus Sep 23, 2019

by Arjun

278 views

0 votes

1 answer

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ISI2014-DCG-53
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$

Arjun asked in Calculus Sep 23, 2019

by Arjun

362 views

1 vote

1 answer

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ISI2015-MMA-77
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$-axis, the line $y=x$, and the line $x=1$. The value of the double integral $ \int \int_R \frac{\sin x}{x}\: dxdy$ is $1-\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$

Arjun asked in Calculus Sep 23, 2019

by Arjun

284 views

1 vote

1 answer

11

ISI2015-DCG-46
Let $I=\int (\sin x – \cos x)(\sin x + \cos x)^3 dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin x + \cos x)^4+K$ $(\sin x + \cos x)^2+K$ $- \frac{1}{4} (\sin x + \cos x)^4+K$ None of these

gatecse asked in Calculus Sep 18, 2019

179 views

1 vote

1 answer

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ISI2015-DCG-51
The area bounded by $y=x^2-4$, $y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$

gatecse asked in Calculus Sep 18, 2019

205 views

1 vote

1 answer

13

ISI2016-DCG-46
Let $I=\int(\sin\:x-\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin\:x+\cos\:x)^{4}+K$ $(\sin\:x+\cos\:x)^{2}+K$ $-\frac{1}{4}(\sin\:x+\cos\:x)^{4}+K$ None of these

gatecse asked in Calculus Sep 18, 2019

203 views

2 votes

1 answer

14

ISI2018-MMA-29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $-2$ $-1$ $1$ $2$

akash.dinkar12 asked in Calculus May 11, 2019

by akash.dinkar12

681 views

1 vote

1 answer

15

ISI2019-MMA-29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$

Sayan Bose asked in Calculus May 7, 2019

1.5k views

1 vote

1 answer

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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 $1/4$ $1/6$ $1/8$ $1/24$

Sayan Bose asked in Calculus May 7, 2019

1.6k views

0 votes

1 answer

17

ISI2019-MMA-25
Let $a,b,c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$

Sayan Bose asked in Calculus May 7, 2019

876 views

0 votes

0 answers

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How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$

`JEET asked in Calculus Jan 20, 2019

by `JEET

292 views

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0 answers

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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.

jhaanuj2108 asked in Calculus Jan 12, 2019

326 views

0 votes

0 answers

20

#integration
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$

amit166 asked in Calculus Jan 3, 2019

169 views

0 votes

0 answers

21

#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosx-cos5x)/10 2.(5sinx-sin5x)/10 3.both 4.none

amit166 asked in Calculus Jan 3, 2019

229 views

7 votes

2 answers

22

TIFR CSE 2019 | Part A | Question: 13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$

Arjun asked in Calculus Dec 18, 2018

by Arjun

1.7k views

1 vote

0 answers

23

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: $0$ $\pi i$ $2 \pi i$ $4 \pi i$

Arjun asked in Others Dec 7, 2018

by Arjun

417 views

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