Register

ISI2021-MMA: 4

• recategorized by
702 views
1 1 vote

If $g’ (x) = f(x)$ then $\int x^{3} f(x^{2}) dx$ is given by

  1. $x^{2} g(x^{2}) – \int xg(x^{2}) dx + C$
  2. $ \frac{1}{2} x^{2} g(x^{2}) – \int xg(x^{2}) dx + C$
  3. $2x^{2} g(x^{2}) – \int xg(x^{2}) dx + C$
  4. $x^{2} g(x^{2}) – \frac{1}{2} \int xg(x^{2}) dx + C$

1 Answer

Voting & Accepting an answer helps improve the community
← Previous · ISI2021-MMA: 5Next → · ISI2021-MMA: 3
← Previous in category · ISI2021-MMA: 6Next in category → · ISI2021-MMA: 1
Position:
Show:

Related questions

1 1 vote
2 2 answers
1.4k
1.4k views
admin asked Jul 23, 2022
1,354 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...
2 2 votes
1 1 answer
695
695 views
admin asked Jul 23, 2022
695 views
ISI2021-MMA: 9
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 interv...
1 1 vote
0 0 answers
538
538 views
admin asked Jul 23, 2022
538 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
714
714 views
admin asked Jul 23, 2022
714 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...