Question:
The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
Show Hint
When solving double integrals, always integrate with respect to one variable first before solving for the other.
Updated On: May 5, 2025
- 12
- 13
- 11
- 14
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
First, we integrate \( x^2 + 3y^2 \) with respect to \( y \), and then integrate the result with respect to \( x \). After solving the double integral, we find that the value is 12.
Was this answer helpful?
0
0
Top Questions on integral
- Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
- Evaluate the integral: \[ \int \sqrt{x^2 + 3x} \, dx \]
Let \( f : (0, \infty) \to \mathbb{R} \) be a twice differentiable function. If for some \( a \neq 0 \), } \[ \int_0^a f(x) \, dx = f(a), \quad f(1) = 1, \quad f(16) = \frac{1}{8}, \quad \text{then } 16 - f^{-1}\left( \frac{1}{16} \right) \text{ is equal to:}\]
- Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
- Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]
View More Questions
Questions Asked in AP PGECET exam
- Starting from \( x_0 = 1 \), one step Newton-Raphson method in solving the equation \( x^3 + 3x - 7 = 0 \) gives the next value as
- AP PGECET - 2024
- Newton Raphson Method
- Peritectic reaction among the following is
- AP PGECET - 2024
- Peritectic Reaction
- In QAM, both ______ of a carrier frequency are varied.
- AP PGECET - 2024
- communication systems
- The following multiplexer gives the logic gate of a/an _____
- AP PGECET - 2024
- Multiplexers
- How many minimum number of flip-flops are required to make a mod-479 counter?
- AP PGECET - 2024
- Timers and counters
View More Questions