Find the integral

Question

Let the:

integral [6 to 10.5] f(x)dx=2

integral [6 to 7.5] f(x)dx=1

integral [9 to 10.5] f(x)dx=5

Find:

integral [7.5 to 9] f(x)dx = ?

and

integral [9 to 7.5] (2f(x)-1)dx = ?

Answer 1

ia)

ntegral [6 to 10.5] f(x)dx=integral [6 to 7.5] f(x)dx+integral [7.5 to 9] f(x)+integral [9 to 10.5] f(x)dx

So integral [7.5 to 9] f(x)d=integral [6 to 10.5] f(x)-integral [6 to 7.5] f(x)-integral [9 to 10.5] f(x)

=2-1-5=-4

b) [9 to 7.5] (2f(x)-1)dx = [7.5 to 9] (-2f(x)+1)dx = -2*+4-[9-7.5]

=8+1.5=9.5

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