Calculus Problem: What's the value of this definite integral
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Calculus Problem: What's the value of this definite integral

[From: ] [author: ] [Date: 11-06-22] [Hit: ]
taking 7dx to be 7x and tried taking the definite of that, but I kept getting 0.£f(x)-8g(x)+7dx= £ f(x)dx-8£g(x)dx+ £7dx. ,= 12-8(5)+7x|(1,= -21-Recall that the definite integral of f(x) from a to b gives us the area under the curve of y = f(x) from a to b.......
Integral from 1 to 2 of f(x) dx = 12. Integral from 1 to 2 of g(x) = g(x)dx = 5.
What is I = integral from 1 to 2 of (f(x) - 8g(x) +7)dx?
The answer is between -19 to -27

I tried plugging in the numbers from the given integrals f(x) and g(x), taking 7dx to be 7x and tried taking the definite of that, but I kept getting 0. Help :(

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Using £ for integral
£f(x)-8g(x)+7dx= £ f(x)dx-8£g(x)dx+ £7dx. , all from 1 to 2

= 12-8(5)+7x|(1,2)
=12-40+(14-7)
= -21

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Recall that the definite integral of f(x) from a to b gives us the area under the curve of y = f(x) from a to b.

We're told in this problem that:

∫[1, 2] f(x) dx = 12 and ∫[1,2] g(x) dx = 5

I = ∫[1,2] f(x) dx - ∫[1,2] 8*g(x) + 7 dx

= 12 - 8(5) + 7 = 19 - 40 = -21
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