Recent questions tagged integration

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1

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

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 63 views

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1 answer

2

ISI2014-DCG-20
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$

asked Sep 23 in Others by Arjun Veteran (425k points) | 22 views

+2 votes

0 answers

3

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 $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 20 views

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4

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

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 12 views

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5

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}$ $1$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 21 views

+1 vote

0 answers

6

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 $1-\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 8 views

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1 answer

7

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

asked Sep 18 in Calculus by gatecse Boss (16.8k points) | 16 views

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1 answer

8

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

asked Sep 18 in Calculus by gatecse Boss (16.8k points) | 12 views

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9

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

asked Sep 18 in Calculus by gatecse Boss (16.8k points) | 12 views

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10

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 (41.9k points) | 57 views

+1 vote

1 answer

11

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 (7.2k points) | 388 views

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1 answer

12

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

asked May 7 in Calculus by Sayan Bose Loyal (7.2k points) | 646 views

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1 answer

13

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 (7.2k points) | 236 views

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0 answers

14

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

asked Jan 20 in Calculus by `JEET Boss (13.8k points) | 97 views

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0 answers

15

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 (197 points) | 82 views

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16

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

asked Jan 3 in Calculus by amit166 Junior (761 points) | 50 views

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0 answers

17

#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) | 68 views

+3 votes

2 answers

18

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 (425k points) | 327 views

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0 answers

19

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

asked Nov 22, 2018 in Calculus by aditi19 Active (5.1k points) | 76 views

+2 votes

1 answer

20

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

asked Nov 22, 2018 in Calculus by Ayush Upadhyaya Boss (27.8k points) | 119 views

0 votes

1 answer

21

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

asked Nov 16, 2018 in Calculus by srestha Veteran (117k points) | 99 views

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0 answers

22

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

asked Nov 14, 2018 in Calculus by aditi19 Active (5.1k points) | 50 views

0 votes

1 answer

23

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

asked Oct 28, 2018 in Calculus by aditi19 Active (5.1k points) | 43 views

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0 answers

24

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

asked Oct 25, 2018 in Calculus by aditi19 Active (5.1k points) | 71 views

0 votes

1 answer

25

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

asked Oct 24, 2018 in Calculus by aditi19 Active (5.1k points) | 112 views

+1 vote

1 answer

26

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 (27.8k points) | 85 views

0 votes

1 answer

27

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

asked Oct 6, 2018 in Calculus by srestha Veteran (117k points) | 101 views

0 votes

0 answers

28

ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$

asked Sep 13, 2018 in Calculus by jothee Veteran (105k points) | 9 views

0 votes

1 answer

29

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) | 45 views

+1 vote

1 answer

30

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 (16.4k points) | 151 views

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