# Simple Integral

## Homework Statement

Ok part of my math homework leads me to do this integral
The integral from 0 to 7 of sqrt((2t-10)^2) dt

## The Attempt at a Solution

The answer is 29, but I can only seem to get -21. I have it = integral of (2t-10)dt, so then I get t^2 - 10t from 0 to 7 = 49-70 = -21. Any help is appreciated. Thanks

Ray Vickson
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## Homework Statement

Ok part of my math homework leads me to do this integral
The integral from 0 to 7 of sqrt((2t-10)^2) dt

## The Attempt at a Solution

The answer is 29, but I can only seem to get -21. I have it = integral of (2t-10)dt, so then I get t^2 - 10t from 0 to 7 = 49-70 = -21. Any help is appreciated. Thanks

If f(t) = sqrt(2t-10)^2), what is f(0)? If g(t) = 2t-10, what is g(0)?

RGV

if y= sqrt(x^2)
Can u simplify y?

Thats agood question Vickson.

Do i need an absolute value somewhere? If I don't simplify as I did and solve with substitution I still get (t-5)**2 from 0 to 7 which still yields -21. Where am I going wrong?

Nvm that last part, I still used sqrt(x^2) = x

Ray Vickson
Homework Helper
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Do i need an absolute value somewhere? If I don't simplify as I did and solve with substitution I still get (t-5)**2 from 0 to 7 which still yields -21. Where am I going wrong?

In my first reply I asked you a question. You still have not answered it. (BTW: I asked for a very good reason!)

RGV

well one is -10 and the other is 10

Ray Vickson
Homework Helper
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OK, so what can you learn from that? Do you, or do you not need to use absolute values?

RGV

i just ended up using x**2 = x*sqrt(x*2), so it keeps its sign and everything works out

Ray Vickson
$$\text{for any real number }r, \; \sqrt{r^2} = |r|.$$