Curve C has equation y=(9+11x)/(3-x-2x^2). Find the area of the curve between the interval (0, 1/2). State your answer in exact terms.
The word "area" should highlight that it is an integration question to the student. The interval asked for is (0,1/2) and so the curve should be integrated between that interval.The first task is to separate the equation into partial fractions, as the denominator seems like a quadratic that could be factorised. Once split into partial fractions of denominators (1-x) and (3+2x), each fraction should be interfrated individually to give:(-4ln(1-x)-3/2ln(3+2x)). This should be evaluated between the values x=0 and x=1/2 since we are finding a definite integral.They have asked for an exact answer so gather the ln terms and state it in the simplified way: 3/2ln(3/4)-4ln(1/2) .
IA
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