19/06/2007VER2-0 (a) Find the Area bounded by the curve y=20sin200  t and the t axis. Between t=0 and t=30ms EXERCISE SET 6 – Area under a Curve & Mean.

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Presentation transcript:

19/06/2007VER2-0 (a) Find the Area bounded by the curve y=20sin200  t and the t axis. Between t=0 and t=30ms EXERCISE SET 6 – Area under a Curve & Mean We can see our curve crosses the x axis at: 0, 5, 10, 15, 20, 25 & 30ms We could break this problem into 6 definite integrals. However we can use symmetry to help solve the problem. Just solve one definite integral & multiply by 6.

19/06/2007VER2-0 (b) Find the area bounded by the curves y=x 3 and y=x. EXERCISE SET 6 – Area under a Curve & Mean Find where the curves intersect. ie solve the equation. x 3 -x=0 x(x 2 -1)=x(x-1)(x+1)=0 ie x = -1, 0, +1 Note we could have used symmetry to help solve this problem.

19/06/2007VER2-0 (c) Find the mean of y=x 2 +2x+1 between x=0 & x=4 EXERCISE SET 6 – Area under a Curve & Mean