Register

ISI2021-MMA: 9

• recategorized by
686 views
2 2 votes

The set of all $a$ satisfying the inequality

$$\frac{1}{\sqrt{a}} \int_{1}^{a} \left( \frac{3}{2} \sqrt{x} + 1 – \frac{1}{\sqrt{x}}  \right) dx < 4$$

Is equal to the interval

  1. $( – 5, – 2)$
  2. $(1, 4)$
  3. $(0, 2)$
  4. $(0, 4)$

1 Answer

0 0 votes

solution:

Voting & Accepting an answer helps improve the community
← Previous · ISI2021-MMA: 10Next → · ISI2021-MMA: 8
← Previous in category · ISI2021-MMA: 13Next in category → · ISI2021-MMA: 6
Position:
Show:

Related questions

1 1 vote
2 2 answers
1.3k
1.3k views
admin asked Jul 23, 2022
1,337 views
ISI2021-MMA: 1
Suppose $f : \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function such that $f(x) = \frac{2 – \sqrt{x+4}}{\sin 2x}$ for all $x \neq 0.$ Then the value of $f(0)$ is...
1 1 vote
1 1 answer
696
696 views
admin asked Jul 23, 2022
696 views
ISI2021-MMA: 4
If $g’ (x) = f(x)$ then $\int x^{3} f(x^{2}) dx$ is given by$x^{2} g(x^{2}) – \int xg(x^{2}) dx + C$$ \frac{1}{2} x^{2} g(x^{2}) – \int xg(x^{2}) dx + C$$2x^{2} g(x^{2}) ...
1 1 vote
0 0 answers
530
530 views
admin asked Jul 23, 2022
530 views
ISI2021-MMA: 13
Let $D$ be the triangular region in the $xy$-plane with vertices at $(0,0), (0,1)$ and $(1, 1).$ Then the value of $$ \iint_{D} \frac{2}{1 + x^{2}} dx dy$$ is$\frac{\pi}{...
0 0 votes
2 2 answers
701
701 views
admin asked Jul 23, 2022
701 views
ISI2021-MMA: 16
The series $$ \sum_{n} \frac{3 \cdot 6 \cdot 9 \cdots 3 n}{7 \cdot 10 \cdot 13 \cdots(3 n+4)} x^{n}, \quad x>0 $$converges for $0<x \leq 1$ and diverges for $x>1$converge...