Integration

Mixed assessment

Work on paper. Suggested time: 40 minutes · 30 written marks. Submit all six answers together. Automatic checking verifies conclusions; method marks require review.

How to enter integrals, curves and constants

Enter expressions only, using x^3/3, sqrt(3*x+1) or x^(3/2). A general antiderivative needs an arbitrary + C; an added fixed number cannot replace it. Equivalent answers may differ by a fixed additive constant. When a point determines the curve, or a definite integral is requested, do not add an arbitrary constant. Use the parameter or variable named beside each field. Enter exact volumes using pi. Give all inputs with commas, pairs as (1,3); (4,2) and intervals as [0,2) U (4,5]. For a line enter a complete equation, such as y=3*x+2 or x=1. Proofs, sketches, limit arguments and written method marks require review.

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