User Soumil Gupta

10 votes

2 answers

1k views

If $f\left(\pi\right)=\pi$ and $\int_{0}^{\pi}\left(f\left(x\right)+f''\left(x\right)\right)\sin x\ dx\ =\ 7\pi$ then find $f\left(0\right)$

asked Oct 2, 2021 at 5:07

7 votes

4 answers

426 views

Conceptual doubt in Definite Integration regarding limits of $\int_{0}^{2}x\cdot\sqrt{x+2}\ dx$

asked Sep 2, 2021 at 11:54

4 votes

4 answers

913 views

Evaluate $\int\frac{3\cot3x-\cot x}{\tan x-3\tan3x}\,dx$

asked Sep 2, 2021 at 7:24

4 votes

1 answer

143 views

Prove that $2^{n}>1+n\sqrt{2^{\left(n-1\right)}}, \ \ \forall n>2$.

asked Feb 20, 2021 at 2:53

3 votes

1 answer

832 views

Extrema points of a non-differentiable function.

asked Aug 6, 2021 at 11:48

3 votes

3 answers

494 views

Intuition behind equation of line in Vector form

asked Oct 20, 2021 at 14:35

3 votes

2 answers

166 views

If $f\left(x\right)=-\frac{x\left|x\right|}{1+x^{2}}$ then find $f^{-1}\left(x\right)$

asked Sep 11, 2021 at 5:32

3 votes

5 answers

492 views

Integrate $\int_{0}^{\infty}\frac{\tan^{-1}x}{x\left(1+x^{2}\right)}dx$ [duplicate]

asked Sep 18, 2021 at 17:07

2 votes

2 answers

161 views

If $f\left(0\right)=1$ and $f'\left(x\right)>3f\left(x\right)\ $ $∀\ x\ \ge0$ then prove that $f\left(x\right)\ge e^{3x}\ ∀\ x\ \ge0$

asked Oct 8, 2021 at 17:28

2 votes

3 answers

804 views

A bag contains $5$ green and $4$ white balls. Three balls are drawn simultaneously. Find the probability that all three balls are green.

asked Nov 1, 2021 at 5:33

2 votes

2 answers

175 views

Calculate $\oint\frac{z^{2}}{z-4}dz$ over a contour C which is a circle with $\left|z\right|=1$ in anticlock-wise direction

asked Jan 29, 2023 at 7:26

2 votes

4 answers

1k views

Finding all $a$ such that $f(x)=\sin2x-8(a+1)\sin x+(4a^2+8a-14)x$ is increasing and has no critical points

asked Aug 14, 2021 at 6:40

2 votes

2 answers

258 views

How to use telescoping series to find: $\sum_{r=1}^{n}\frac{1}{r+2}$ [closed]

asked Feb 22, 2021 at 2:44

1 vote

1 answer

94 views

Let $p\left(x\right)=x^{2}+bx+c=0$ and equation $p\left(p\left(p\left(x\right)\right)\right)=0$ have a common root then:

asked Feb 21, 2021 at 4:19

1 vote

0 answers

52 views

Find the coefficient of $x^{9\ }$ in$\left(1+x\right)\left(1+x^{2}\right)\left(1+x^{3}\right)...\left(1+x^{100}\right)$ [duplicate]

asked Mar 1, 2021 at 13:13

1 vote

1 answer

90 views

Prove that $\frac{1}{1⋅2}+\frac{1}{3⋅4}+\frac{1}{5⋅6}+....+\frac{1}{199⋅200}$ = $\frac{1}{101}+\frac{1}{102}+\frac{1}{103}...+\frac{1}{200}$ [duplicate]

asked May 6, 2021 at 10:15

1 vote

1 answer

84 views

Substitution in differentiation

asked Aug 21, 2021 at 13:48

1 vote

1 answer

121 views

For what integral values of $x$ is $\left|x^{3}-6x^{2}+11x-6\right|$ prime?

asked May 14, 2021 at 7:47

1 vote

2 answers

117 views

Can we use Proof by Induction to extend DeMorgan's Law to Infinite Number of Sets?

asked Aug 24, 2023 at 6:27

1 vote

2 answers

89 views

Why does the triangle inequality not work here?

asked Feb 2, 2022 at 2:12

1 vote

1 answer

183 views

Confusion with the term 'Area bounded by the curves'

asked Sep 20, 2021 at 6:40

1 vote

4 answers

162 views

Find $\lim_{x\to0^+}\ x\left(\ln x\right)^{2}$

asked Oct 1, 2021 at 17:22

0 votes

1 answer

52 views

Prove that a solution of $y_{1}y_{3}=3y_{2}^{2}$ can be $x=A_{1}y+A_{2}$ and $x=A_{1}y^{2}+A_{2}y+A_{3}$

asked Oct 12, 2021 at 16:49

0 votes

1 answer

347 views

$f\left(x\right) = \int_{1}^{x}\frac{\sin(x)\cos(y)\mathrm{d}y}{y^{2}+y+1}$, find solution of $f'\left(x\right)=0$

asked Sep 9, 2021 at 3:03

0 votes

2 answers

659 views

If $b>0$ then find the number of values of'a' for which domain and range of $f\left(x\right)=\sqrt{ax^{2}+bx}$ are equal.

asked Sep 9, 2021 at 17:29

0 votes

1 answer

107 views

How do I convert logic to set theory

asked Nov 6, 2021 at 12:31

0 votes

0 answers

81 views

Doubt in Probability question

asked Nov 8, 2021 at 5:38

0 votes

2 answers

50 views

Range of an increasing function

asked May 22, 2021 at 4:54

0 votes

2 answers

90 views

Problem on binomial coefficients [duplicate]

asked May 26, 2021 at 17:42

0 votes

4 answers

130 views

Find the range of $\left|\left|\sin x\right|\cos x+\sin x\left|\cos x\right|\right|$ [closed]

asked Jun 8, 2021 at 7:08

Stack Exchange Network

36 Questions

If $f\left(\pi\right)=\pi$ and $\int_{0}^{\pi}\left(f\left(x\right)+f''\left(x\right)\right)\sin x\ dx\ =\ 7\pi$ then find $f\left(0\right)$

Conceptual doubt in Definite Integration regarding limits of $\int_{0}^{2}x\cdot\sqrt{x+2}\ dx$

Evaluate $\int\frac{3\cot3x-\cot x}{\tan x-3\tan3x}\,dx$

Prove that $2^{n}>1+n\sqrt{2^{\left(n-1\right)}}, \ \ \forall n>2$.

Extrema points of a non-differentiable function.

Intuition behind equation of line in Vector form

If $f\left(x\right)=-\frac{x\left|x\right|}{1+x^{2}}$ then find $f^{-1}\left(x\right)$

Integrate $\int_{0}^{\infty}\frac{\tan^{-1}x}{x\left(1+x^{2}\right)}dx$ [duplicate]

If $f\left(0\right)=1$ and $f'\left(x\right)>3f\left(x\right)\ $ $∀\ x\ \ge0$ then prove that $f\left(x\right)\ge e^{3x}\ ∀\ x\ \ge0$

A bag contains $5$ green and $4$ white balls. Three balls are drawn simultaneously. Find the probability that all three balls are green.

Calculate $\oint\frac{z^{2}}{z-4}dz$ over a contour C which is a circle with $\left|z\right|=1$ in anticlock-wise direction

Finding all $a$ such that $f(x)=\sin2x-8(a+1)\sin x+(4a^2+8a-14)x$ is increasing and has no critical points

How to use telescoping series to find: $\sum_{r=1}^{n}\frac{1}{r+2}$ [closed]

Let $p\left(x\right)=x^{2}+bx+c=0$ and equation $p\left(p\left(p\left(x\right)\right)\right)=0$ have a common root then:

Find the coefficient of $x^{9\ }$ in$\left(1+x\right)\left(1+x^{2}\right)\left(1+x^{3}\right)...\left(1+x^{100}\right)$ [duplicate]

Prove that $\frac{1}{1⋅2}+\frac{1}{3⋅4}+\frac{1}{5⋅6}+....+\frac{1}{199⋅200}$ = $\frac{1}{101}+\frac{1}{102}+\frac{1}{103}...+\frac{1}{200}$ [duplicate]

Substitution in differentiation

For what integral values of $x$ is $\left|x^{3}-6x^{2}+11x-6\right|$ prime?

Can we use Proof by Induction to extend DeMorgan's Law to Infinite Number of Sets?

Why does the triangle inequality not work here?

Confusion with the term 'Area bounded by the curves'

Find $\lim_{x\to0^+}\ x\left(\ln x\right)^{2}$

Prove that a solution of $y_{1}y_{3}=3y_{2}^{2}$ can be $x=A_{1}y+A_{2}$ and $x=A_{1}y^{2}+A_{2}y+A_{3}$

$f\left(x\right) = \int_{1}^{x}\frac{\sin(x)\cos(y)\mathrm{d}y}{y^{2}+y+1}$, find solution of $f'\left(x\right)=0$

If $b>0$ then find the number of values of'a' for which domain and range of $f\left(x\right)=\sqrt{ax^{2}+bx}$ are equal.

How do I convert logic to set theory

Doubt in Probability question

Range of an increasing function

Problem on binomial coefficients [duplicate]

Find the range of $\left|\left|\sin x\right|\cos x+\sin x\left|\cos x\right|\right|$ [closed]