Question

Calculus 2 - Indefinite Integrals

Answer 1

Make the substitution (x-5) = t
f(x-5) = f(t) and dx = dt
when x = a+5, t = a
when x = b+5, t = b

Answer 2

\[\Large \int\limits_{a+5}^{b+5}f(x)dx = \int\limits_{a}^{b}f(t)dt\]

Answer 3

ok, so I plug in the values into that equation?

Answer 4

They have given you the value for the right hand side. Remember this is a definite integral which means the answer is a number and it wouldn't matter if the variable is called x or t or u. So think of the variable t on the right hand side as x and see if they have give you the value for this integral.

Answer 5

sorry, i really suck at this stuff

Answer 6

so equals 2?

Answer 7

\[\Large \int\limits\limits_{a}^{b}f(t)dt \quad \text{ is same as } \int\limits\limits_{a}^{b}f(x)dx = ?\]

Answer 8

Look at the value of the first integral they have provided in the problem.

Answer 9

8

Answer 10

yes!

Answer 11

Essentially what they have done in this problem is shifted the graph f(x) five units to the right which changes the function to f(x-5) and they have accordingly shifted the limits a and b also five units to the right thus giving the same area under the curve as before.

Answer 12

So the answer to this problem is 8.

Answer 13

gothca, thanks

Answer 14

You are welcome.