Recent questions tagged integration

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1

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 $-2$ $-1$ $1$ $2$

asked May 11 in Calculus by akash.dinkar12 Boss (40.5k points) | 33 views

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1 answer

2

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 $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$

asked May 7 in Calculus by Sayan Bose Loyal (6.9k points) | 347 views

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1 answer

3

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 $(0,2)$

asked May 7 in Calculus by Sayan Bose Loyal (6.9k points) | 203 views

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4

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

asked Jan 20 in Calculus by `JEET Active (3.4k points) | 86 views

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5

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.

asked Jan 12 in Calculus by jhaanuj2108 (227 points) | 67 views

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6

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

asked Jan 3 in Calculus by amit166 Junior (761 points) | 47 views

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7

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

asked Jan 3 in Calculus by amit166 Junior (761 points) | 65 views

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8

TIFR2019-A-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 ? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$

asked Dec 18, 2018 in Calculus by Arjun Veteran (400k points) | 177 views

+3 votes

1 answer

9

TIFR GS 2019
How to solve it$?$ $\int_{0}^{1}\frac{x^{300}}{(x^{3}+x^{2}+1)}dx$ a.0.00 b.0.33 c.0.02 d.0.03 d.0.04 two decimal digit

asked Dec 9, 2018 in Calculus by amit166 Junior (761 points) | 531 views

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10

Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$

asked Nov 22, 2018 in Calculus by aditi19 Active (3.5k points) | 71 views

+2 votes

1 answer

11

Calculus-Integration
$\int x^7.e^{x^4}dx$ How to do this?

asked Nov 22, 2018 in Calculus by Ayush Upadhyaya Boss (25.4k points) | 111 views

0 votes

1 answer

12

Integration
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$

asked Nov 16, 2018 in Calculus by srestha Veteran (114k points) | 87 views

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13

Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$

asked Nov 14, 2018 in Calculus by aditi19 Active (3.5k points) | 46 views

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1 answer

14

Gilbert Strang
Differentiate y=$x^{-1/lnx}$

asked Oct 28, 2018 in Calculus by aditi19 Active (3.5k points) | 42 views

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15

Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$

asked Oct 25, 2018 in Calculus by aditi19 Active (3.5k points) | 66 views

0 votes

1 answer

16

Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$

asked Oct 24, 2018 in Calculus by aditi19 Active (3.5k points) | 104 views

+1 vote

1 answer

17

Calculus-Definite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$

asked Oct 13, 2018 in Calculus by Ayush Upadhyaya Boss (25.4k points) | 74 views

0 votes

1 answer

18

Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$

asked Oct 6, 2018 in Calculus by srestha Veteran (114k points) | 97 views

0 votes

1 answer

19

Area between curves
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is . I am getting $128√2$.

asked Sep 3, 2018 in Calculus by Jason Active (1.5k points) | 36 views

0 votes

1 answer

20

Definite Integral
S = $\int_{0}^{2\Pi } \sqrt{4cos^{2}t +sin^{2}t} \, \, dt$ Please explain how to solve it.

asked Jun 11, 2018 in Calculus by ankitgupta.1729 Boss (11.3k points) | 133 views

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0 answers

21

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)

asked May 18, 2018 in Calculus by srestha Veteran (114k points) | 202 views

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0 answers

22

Integration
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$

asked Apr 28, 2018 in Calculus by kd..... Junior (917 points) | 72 views

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0 answers

23

Multiple integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration

asked Apr 28, 2018 in Calculus by kd..... Junior (917 points) | 59 views

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3 answers

24

Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$

asked Apr 24, 2018 in Calculus by srestha Veteran (114k points) | 115 views

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0 answers

25

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

asked Apr 24, 2018 in Calculus by Tesla! Boss (18.6k points) | 129 views

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26

Calculus Integration
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$

asked Apr 24, 2018 in Calculus by kd..... Junior (917 points) | 106 views

0 votes

1 answer

27

ISI-2014-07
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is $2\sqrt2\pi^2$ $\dfrac{\pi^2}{2\sqrt2}$ $\dfrac{\pi^2}{\sqrt2}$ $\sqrt2\pi^2$

asked Mar 17, 2018 in Mathematical Logic by jjayantamahata Active (1.8k points) | 105 views

0 votes

3 answers

28

ISI-2014-5
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$ $\text{is 0}$ $\text{is 1}$ $\text{is 2}$ $\text{does not exist}$

asked Mar 17, 2018 in Mathematical Logic by jjayantamahata Active (1.8k points) | 125 views

+1 vote

1 answer

29

EE: GATE 2018 Maths - 18(Electrical Engineering)
Let $f$ be a real-valued function of a real variable defined as $f(x) = x - [ x ]$ , where $ [ x ]$ denotes the largest integer less than or equal to $x$. The value of ${\LARGE \int}_{0.25}^{1.25} \! f(x) \, \mathrm{d}x$ is ---------- (upto $2$ decimal places).

asked Feb 21, 2018 in Calculus by Lakshman Patel RJIT Boss (36.3k points) | 212 views

+7 votes

6 answers

30

GATE2018-16
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____

asked Feb 14, 2018 in Calculus by gatecse Boss (18.2k points) | 3.9k views

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