What is the integral of sqrt x 2 y 2?

The indefinite integral of sqrt(x^2y^2) with respect to x is x^2y/2 + c, assuming that x and y are independent variables. The definite integral of this function between x = a and x = b is b^2y/2 - a^2y/2.

The first step in calculating this integral is to simplify sqrt(x^2y^2) to xy. One can then integrate xy with respect to x using the normal rule of integration: increase the exponent of x by 1, and then divide the result by this new exponent. If y depends on x, then one must substitute the expression for y in terms of x into the integrand xy before integrating.