Question:
The value of the integral
\[\int_{0}^{\sqrt{8}} \int_{x^2}^{\sqrt{8 - x^2}} \frac{3\sqrt{x^2 + y^2}}{\sqrt{8}} \, dy \, dx \]
is equal to __________ (answer in integer).
The value of the integral
\[\int_{0}^{\sqrt{8}} \int_{x^2}^{\sqrt{8 - x^2}} \frac{3\sqrt{x^2 + y^2}}{\sqrt{8}} \, dy \, dx \]
is equal to __________ (answer in integer).
\[\int_{0}^{\sqrt{8}} \int_{x^2}^{\sqrt{8 - x^2}} \frac{3\sqrt{x^2 + y^2}}{\sqrt{8}} \, dy \, dx \]
is equal to __________ (answer in integer).
Updated On: Oct 1, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 2
Solution and Explanation
The correct Answer is : 2-2(Approx.)
Was this answer helpful?
0
0
Top Questions on Integral Calculus
- Let $\beta(m, n) = \int_{0}^{1}x^{m-1}(1-x)^{n-1}dx$, $m, n > 0$. If $\int_{0}^{1}(1-x^{10})^{20}dx = a\beta(b,c)$, then $100(a+b+x)$ equals
- JEE Main - 2024
- Mathematics
- Integral Calculus
- If \[ \int \frac{1}{\sqrt[5]{(x - 1)^4}(x + 3)^6} \, dx = A \left( \frac{\alpha x - 1}{\beta x + 3} \right)^B + C, \] where \(C\) is the constant of integration, then the value of \(\alpha + \beta + 20AB\) is _______.
- JEE Main - 2024
- Mathematics
- Integral Calculus
- Let \( \int \frac{2 - \tan x}{3 + \tan x} \, dx = \frac{1}{2} \left( \alpha x + \log_e \lvert \beta \sin x + \gamma \cos x \rvert \right) + C \), where \( C \) is the constant of integration.
- JEE Main - 2024
- Mathematics
- Integral Calculus
- Let the function \(f:[1,\infin)β\R\) be defined by
\(f(t) = \begin{cases} (-1)^{n+1}2, & \text{if } t=2n-1,n\in\N, \\ \frac{(2n+1-t)}{2}f(2n-1)+\frac{(t-(2n-1))}{2}f(2n+1) & \text{if } 2n-1<t<2n+1,n\in\N. \end{cases}\)
Define \(g(x)=\int\limits_{1}^{x}f(t)dt,x\in(1,\infin).\) Let Ξ± denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and \(Ξ²=\lim\limits_{xβ1+}\frac{g(x)}{x-1}\). Then the value of Ξ± + Ξ² is equal to _____.- JEE Advanced - 2024
- Mathematics
- Integral Calculus
- The value of
\(\lim\limits_{tβ\infin}\left((\log(t^2+\frac{1}{t^2}))^{-1} \int\limits_{1}^{\pi t} \frac{\sin^25x}{x}dx\right)\)
equals ___________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Multivariable Calculus
- Integral Calculus
View More Questions
Questions Asked in IIT JAM MS exam
- A bag has 5 blue balls and 15 red balls. Three balls are drawn at random from the bag simultaneously. Then the probability that none of the chosen balls is blue equals
- IIT JAM MS - 2024
- Probability
- Let the random vector \( (X, Y) \) have the joint probability density function
\[f(x, y) = \begin{cases} \frac{1}{x}, & \text{if } 0 < y < x < 1 \\0, & \text{otherwise} \end{cases}.\]
Then \( \text{Cov}(X, Y) \) is equal to:- IIT JAM MS - 2024
- Probability
- Two factories \( F_1 \) and \( F_2 \) produce cricket bats that are labelled. Any randomly chosen bat produced by factory \( F_1 \) is defective with probability 0.5 and any randomly chosen bat produced by factory \( F_2 \) is defective with probability 0.1. One of the factories is chosen at random, and two bats are randomly purchased from the chosen factory. Let the labels on these purchased bats be \( B_1 \) and \( B_2 \). If \( B_1 \) is found to be defective, then the conditional probability that \( B_2 \) is also defective is equal to __________ (round off to 2 decimal places).
- IIT JAM MS - 2024
- Probability
- Consider a coin for which the probability of obtaining head in a single toss is \( \frac{1}{3} \). Sunita tosses the coin once. If head appears, she receives a random amount of \( X \) rupees, where \( X \) has the \( \text{Exp}\left( \frac{1}{9} \right) \) distribution. If tail appears, she loses a random amount of \( Y \) rupees, where \( Y \) has the \( \text{Exp}\left( \frac{1}{3} \right) \) distribution. Her expected gain (in rupees) is equal to __________ (answer in integer).
- IIT JAM MS - 2024
- Probability
- If 12 fair dice are independently rolled, then the probability of obtaining at least two sixes is equal to __________ (round off to 2 decimal places)
- IIT JAM MS - 2024
- Probability
View More Questions