For some strange reason, I just can't seem to get the answer to these integration problems. It's the fact that they should be incredibly simple that's worrying; I must be making an obvious mistake without realising it. Could someone help me out by going through them with me?
Number one;
Find the area bounded by the curve y = x2 - x - 2, the x-axis and the lines x = 1 and x = 3.
My working
= [2∫3 x2 - x - 2] + [|1∫2 x2 - x - 2|]
= [x3/3 - x2/2 - 2x]23 + [|x3/3 - x2/2 - 2x|]12
= [{(3)3/3 - (3)2/2 - 2(3)} - {(2)3/3 - (2)2/2 - 2(2)}] + [|{(2)3/3 - (2)2/2 - 2(2)} - {(1)3/3 - (1)2/2 - 2(1)}|]
Number two;
Evaluate 0∫1 x3(x4 - 3) dx by using the substitution u = x4
Number one;
Find the area bounded by the curve y = x2 - x - 2, the x-axis and the lines x = 1 and x = 3.
My working
= [2∫3 x2 - x - 2] + [|1∫2 x2 - x - 2|]
= [x3/3 - x2/2 - 2x]23 + [|x3/3 - x2/2 - 2x|]12
= [{(3)3/3 - (3)2/2 - 2(3)} - {(2)3/3 - (2)2/2 - 2(2)}] + [|{(2)3/3 - (2)2/2 - 2(2)} - {(1)3/3 - (1)2/2 - 2(1)}|]
Number two;
Evaluate 0∫1 x3(x4 - 3) dx by using the substitution u = x4
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