Recent questions tagged definite-integration

0 votes

1 answer

1

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) | 21 views

+2 votes

0 answers

2

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

0 votes

0 answers

3

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) | 11 views

0 votes

0 answers

4

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

0 votes

0 answers

5

ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 9 views

0 votes

0 answers

6

ISI2015-MMA-76
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$ is $\sqrt{\pi/3}$ $\pi/\sqrt{3}$ $\sqrt{2 \pi/3}$ $2 \pi / \sqrt{3}$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 7 views

0 votes

1 answer

7

ISI2015-MMA-78
The value of $\underset{n \to \infty}{\lim} \bigg[ (n+1) \int_0^1 x^n \text{ln}(1+x) dx \bigg]$ is $0$ $\text{ln }2$ $\text{ln }3$ $\infty$

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

0 votes

0 answers

8

ISI2015-MMA-80
Let $0 < \alpha < \beta < 1$. Then $ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$ is equal to $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$

asked Sep 23 in Calculus by Arjun Veteran (425k points) | 14 views

0 votes

0 answers

9

ISI2015-MMA-81
If $f$ is continuous in $[0,1]$ then $\underset{n \to \infty}{\lim} \Sigma_{j=0}^{[n/2]} \frac{1}{n} f \bigg(\frac{j}{n} \bigg)$ (where $[y]$ is the largest integer less than or equal to $y$) does not exist exists and is equal to $\frac{1}{2} \int_0^1 f(x) dx$ exists and is equal to $ \int_0^1 f(x) dx$ exists and is equal to $\int_0^{1/2} f(x) dx$

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

0 votes

1 answer

10

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

0 votes

0 answers

11

ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$

asked Sep 18 in Linear Algebra by gatecse Boss (16.8k points) | 9 views

0 votes

1 answer

12

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

0 votes

0 answers

13

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

+1 vote

0 answers

14

Virtual Gate Test Series: Calculus - Definite Integration
$\int \limits_0^1 (1 + y^2)^{-1.5} dy=?$

asked Jan 31, 2018 in Calculus by Utsav09 Active (1.2k points) | 110 views

+2 votes

3 answers

15

integration
$\int_{-4}^{4}|3-x|dx$ a) 13 b)8 c)25 d)24

asked Nov 11, 2017 in Calculus by Parshu gate Active (3.1k points) | 202 views

+2 votes

1 answer

16

integration question
$f(x) = \int_{- \infty}^{\infty} f(x) e^{2\pi x} dx$ solve f(x)

asked Oct 11, 2017 in Calculus by Pavan Kumar Munnam Boss (10.7k points) | 621 views

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

Recent questions tagged definite-integration

Recent Posts

Recent Blog Comments