- Anonymous1 month ago
Given: a→b∫ f(x) dx = 3 and c→b∫ f(x) dx = 5
If c→b∫ f(x) dx = 5 then
b→c∫ f(x) dx = -5
a→c∫ f(x) dx = [a→b∫ f(x) dx] + [b→c∫ f(x) dx]
a→c∫ f(x) dx =  + [-5] = -2
- Steve4PhysicsLv 71 month ago
The question has errors:
‘dx’ is missing from each integral.
The instructions make no sense.
7 marks for a single question you can do in your head is silly.
Each integral has the lower limit on the bottom. So we can tell a<b, c<b and a<c.
That means the limit values in increasing order are: a, c, b.
Imagine points on the x-axis, left to right: x=a, x=c, x=b
Each integral is equal to the area under the f(x) curve between the given limits. So we know:
(area from a to c) + (area from c to b) = (area from a to b)
(area from a to c) = (area from a to b) - (area from c to b)
. . . . . . . . . . . . . . .= 3 – 5 = -2
(The negative sign idicates area below the x-axis)