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(Solved): Problem 2. Let D be the triangle with vertices (0,0),(B,3B) and (2B,2B), where B is some positive c ...
Problem 2. Let be the triangle with vertices and , where is some positive constant. Write the double integral as a sum of two iterated integrals (a) with the order of integration , (b) with the order of integration .
Expert Answer
First, we need to evaluate the double integral, we need to first determine the limits of integration for both orders.(a) Order of integration In this case, we integrate over x first, then over y The limits of integration for x and y depend on the equations of the lines that form the boundary of the triangle.* The line passing through has has As we know the equation of the line passing through two points is so so, here substitute these value in equation (2) Point-slope formula: Where m is the slope of the line. The numerical value for slope can be expressed as a ratio or fraction. The numerator will contain the difference of y-values, and the denominator will contain the difference of x-values. The above slope formula is conceptually defined as the rise overrun.