Yes, it is wrong. It is standard "Calculus I" mistake to treat a function of the variable as if it were just the variable but you should be past that by the time you are doing multiple integrals. "[itex]1/(1+ y^2)[/itex]" is NOT the same as [itex]1/y[/itex] and its anti-derivative is not a logarithm. The anti-derivative of [itex]1/(1+ y^2)[/itex] is [itex]arctan(y)+ C[/itex]. That's a standard anti-derivative that you should have memorized.emelie_earl said:
My idea was that the limits are
and that the anti-derivative of dy was
xlog(1+y^2)
but that seems wrong...
Yes, reversing the order of integration is the best way to handle this one. Integerating [itex]arctan(1)- arctan(x^2)= \pi/4- arctan(x^2)[/itex] is likely to be very difficult!maybe use these limits instead
and start with dx?
gives us
then we take dy
guess, i figured it out eventually with the help of wolfram with the last integration
Yes. I agree !HallsofIvy said:
A double integral problem is a type of mathematical problem involving the integration of a function over a two-dimensional area or region. It is often used to calculate the volume under a surface or to find the area between two curves.
A single integral involves the integration of a function along a one-dimensional interval, while a double integral involves the integration of a function over a two-dimensional region. In other words, a double integral is like the extension of a single integral into another dimension.
The solution to a double integral problem involves breaking down the problem into smaller, simpler integrals using one of several methods, such as iterated integration, polar coordinates, or using a change of variables. The resulting integrals are then solved using basic integration techniques.
Double integrals have many applications in mathematics, physics, and engineering. They are used to calculate volumes, areas, and averages, as well as to solve problems involving mass, force, and probability in two-dimensional systems. They are also used in multivariable calculus and vector calculus.
Yes, some common mistakes when solving double integral problems include incorrect setup of the integral, incorrect choice of limits of integration, and errors in the calculation of the integrals. It is important to carefully follow the steps and check for errors, especially when changing variables or using non-standard methods of solving the integral.