- #1
LagrangeEuler
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Homework Statement
Solve double integral
[tex]\int^1_0\int^1_x\sin(y^2)dydx[/tex]
Homework Equations
The Attempt at a Solution
I got with Wolfram Mathematica 7.0 result 0.23 numerically. Can it be solved analyticaly?
Yes, it can be solved analytically. Change the order of integration.LagrangeEuler said:Homework Statement
Solve double integral
[tex]\int^1_0\int^1_x\sin(y^2)dydx[/tex]
Homework Equations
The Attempt at a Solution
I got with Wolfram Mathematica 7.0 result 0.23 numerically. Can it be solved analyticaly?
LagrangeEuler said:I'm not sure how?
LagrangeEuler said:I'm not sure how?
Dick said:Draw the region you are integrating over. It's a triangle in the xy plane, right? Then just set the integration up so you do dx first then dy.
To solve a double integral numerically, you can use numerical integration methods such as the trapezoidal rule or Simpson's rule. These methods involve breaking the double integral into smaller, simpler integrals and then summing them together to approximate the value.
Yes, a double integral can be solved analytically if the function and the limits of integration are simple enough. Analytical solutions involve using mathematical techniques such as substitution, integration by parts, or trigonometric identities to evaluate the integral.
Numerical solutions allow for quick and easy approximations of the value of a double integral. They also do not require advanced mathematical knowledge or techniques, making them accessible to a wider range of individuals.
Yes, there can be limitations to solving a double integral numerically. If the function is very complex or has discontinuities, numerical methods may not provide an accurate solution. Additionally, numerical methods can be time-consuming and may require a large number of iterations to achieve a desired level of accuracy.
No, a double integral involves integrating a function of two variables over a region in two-dimensional space. Therefore, a double integral cannot be solved with only one variable.