Find the area bounded by the curve x^3-3x^2+2x and the x-axis between x=0 and x=1.
To find the area under a curve that is bounded by the x-axis you simply need to integrate the equation of the curve between the limits, so for this equation we will integrate y=x3-3x2+2x with 1 as our upper limit and 0 as our lower limit. To integrate an expression you add 1 to the power and divide by the new power, so the integral of x3-3x2+2x is (1/4)x4-x3+x2. We then substitute x=1 and x=0 into the expression and subtract the resulting values from eachother. When x=1, (1/4)x4-3x3+x2=1/4 and when x=0, (1/4)x4-3x3+x2=0. (1/4)-0=1/4 and so that is our final answer to the question.
