Find the area under the curve y=xsin(x), between the limits x=-pi/2 and x=pi/2.

We are going to need to use integration for this problem as it involves finding an area under a curve. Also notice that y is a product of two functions of x ; x and sin(x). This means in this particular case the method of integration by parts will be needed. Firstly, we need to indentify which parts of the function y corresspond to the different components of the intergration by parts formula. Then coresspondingly subsistute them into the formula.Once this is completed it becomes a simple case of integrating the function cos(x) between the two limits in the question giving an answer of 2.