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Recent questions tagged integration

0 votes
1 answer
2
2 votes
1 answer
3
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, 2019 in Calculus Arjun 220 views
3 votes
1 answer
4
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, 2019 in Calculus Arjun 144 views
0 votes
1 answer
5
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, 2019 in Calculus Arjun 124 views
0 votes
1 answer
6
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, 2019 in Calculus Arjun 204 views
1 vote
0 answers
7
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, 2019 in Calculus Arjun 109 views
0 votes
1 answer
8
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, 2019 in Calculus gatecse 66 views
0 votes
1 answer
9
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, 2019 in Calculus gatecse 107 views
1 vote
1 answer
10
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, 2019 in Calculus gatecse 92 views
2 votes
1 answer
11
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, 2019 in Calculus akash.dinkar12 360 views
1 vote
1 answer
12
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, 2019 in Calculus Sayan Bose 786 views
0 votes
1 answer
13
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, 2019 in Calculus Sayan Bose 1.1k views
0 votes
1 answer
14
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, 2019 in Calculus Sayan Bose 572 views
0 votes
0 answers
15
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
asked Jan 20, 2019 in Calculus `JEET 154 views
0 votes
0 answers
16
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, 2019 in Calculus jhaanuj2108 193 views
0 votes
0 answers
17
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$
asked Jan 3, 2019 in Calculus amit166 100 views
0 votes
0 answers
18
$I=\int sin(2x) cos(3x) dx$ 1.(5cosx-cos5x)/10 2.(5sinx-sin5x)/10 3.both 4.none
asked Jan 3, 2019 in Calculus amit166 127 views
5 votes
2 answers
19
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 Arjun 959 views
1 vote
0 answers
20
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: $0$ $\pi i$ $2 \pi i$ $4 \pi i$
asked Dec 7, 2018 in Others Arjun 255 views
1 vote
1 answer
21
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: $2 \pi$ $4 \pi$ $-4 \pi$ $8 \pi$
asked Dec 7, 2018 in Others Arjun 208 views
0 votes
0 answers
22
2 votes
1 answer
23
$\int x^7.e^{x^4}dx$ How to do this?
asked Nov 22, 2018 in Calculus Ayush Upadhyaya 191 views
0 votes
1 answer
24
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
asked Nov 16, 2018 in Calculus srestha 238 views
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