sean asked in Science & MathematicsMathematics · 1 month ago

# solve this?

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• Anonymous
1 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 = [3] + [-5] = -2

• 1 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.

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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)