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total area

summer1854
in Analysis and Calculus

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hi, i have the answer to this problem, but can't figure out how they did it.

 

find the total area of the region bounded by the graph of y=x[(1-x^2)^(1/2)] and the x axis.

Graph it. Break the graph into parts(parts where it is above the x-axis and below). Or you could plug in x=0 to find the x-intercepts and use test points to find the regions. Once you find the regions above and below the x-axis, you will have your limits of integration. Add the integrations of the positive portions of the graphs and subtract the integration of the negative portion of the graph.

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