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

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Homework Help Overview

The problem involves integrating the expression (sin²(t) + cos²(t) - 1) from e^x to e^(2x). The original poster seeks clarification on whether the expression simplifies due to trigonometric identities or if it should be approached as a standard integration problem.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the expression, with some questioning if it simplifies to zero due to the identity sin²(t) + cos²(t) = 1. Others express uncertainty about the integration limits and the implications of the expression being zero.

Discussion Status

The discussion is exploring different interpretations of the integral and the implications of the trigonometric identity. Some participants have provided hints and guidance, but there is no explicit consensus on the correct approach or interpretation of the limits.

Contextual Notes

There is mention of limits of integration from e^x to e^(2x) and a reference to another integral problem that may be unrelated. Participants express varying levels of confidence and confusion regarding the problem setup.

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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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