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Suppose, f(x)dx=8 (f(x)dx)^2=12 g(t)dt=2 (g(t)dt)^2=3 These all have the integral of a to b. Evaluate the integral between a+5 to b+5 f(x-5)dx.
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i think most of that has nothing to do with the problem
you want \[\int_{a+5}^{b+5}f(x-5)dx\] right?
make a u sub \(u=x-5\)
Nope there's an actual number lol.
At first I was thinking of something along the lines of shifting it to the right horizontally but idk.
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Are you still having trouble with @satellite73 suggestion?
2nd fundamental thm of calculus \[\int\limits_{a+5}^{b+5} f(u) du = F(u) = F(x-5) = F(b) -F(a) = 8\]
graphically, you shifted the function to right 5 units but also are evaluating at limits that have also been shifted 5 to right. So you get the same area
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