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I require full, detailed, step by step workings for all sections of this problem
a) For the curve with the equation y = x^3 + 3x^2 - 2
i) Find the position and nature of any stationary points.
ii) Make up tables of signs for y, y' and y''. Use these to help you make a sketch of the curve.
b) Using your sketch of the curve y = x^3 + 3x^2 - 2
i) Shade in the region representing S x^3 + 3x^2 - 2 dx 1 ---> -3
ii) Without evaluating the integral, explain why its value is zero.
iii) Evaluate the integral to confirm your answer.
Questions about curve sketching, integration, stationary points and asymptotes are answered in detail. The solution is comprehensive and well presented.