Integrate int (sin^2(t) + cos^2(t) -1)dt from e^x to e^(2x)

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Homework Statement



Integrate from e^x to e^2x: (sin^2(t) + cos^2(t) -1)dt

Homework Equations


just standard integral equations


The Attempt at a Solution



I know how to do most of it, my only question is: is (sin^2(e^2x) + cos^2(e^x) -1) a special trig identity? or would i just solve it like a normal interation in parts problem?
 
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well it seems trivial to me... lol
This question seems to be just tricky, nothing else.
 
Aren't the sin and cos together adding to 1 the way you've written it, thus 1-1=0 ? You may want to double check you have it correct
 
\int_{e^{x}}^{e^{2x}}(sin^{2}(t)+cos^{2}(t)-1)dt=\int_{e^{x}}^{e^{2x}}(1-1)dt=\int_{e^{x}}^{e^{2x}}(0)dt=?

What does this equal to??
 
ok, thanks guys lol. I feel dumb now
 
cooltee13 said:
ok, thanks guys lol. I feel dumb now

Ok, integrate the following:

\int_0^{ln(1)} sin(x)e^{-x^{2}}dx

This question was somewhere i don't know where though. Give a shot to it.

HINT: THis is also tricky.
 
Last edited:
sutupidmath said:
\int_{e^{x}}^{e^{2x}}(sin^{2}(t)+cos^{2}(t)-1)dt=\int_{e^{x}}^{e^{2x}}(1-1)dt=\int_{e^{x}}^{e^{2x}}(0)dt=?

What does this equal to??
Isnt that just equal to 1?
 
Look at your limits of Integration

From 0 to Ln(1)
 
cooltee13 said:
Isnt that just equal to 1?

Why on Earth do u think it is equal to 1?
 
  • #10
rocomath said:
Look at your limits of Integration

From 0 to Ln(1)
How did u change your display name?
 
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