# Is $\int\left(\sin^2x + \cos^2x\right)\;dx = \int 1 \; dx$ ?

I have just begun my 2nd calculus course and so far have just been applying the substitution method for solving anti derivatives and other basic rules.

I have a question that is probably very easy to answer.

Is $\displaystyle\int \left(\sin^2x + \cos^2x\right)\;dx = \int 1 \; dx$ ?

Thanks, Sam

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Pythagorean Theorem... (yes, just with algebra: $\sin^2 x+\cos^2 x=1$). –  David Mitra Feb 8 '12 at 22:39
The trigonometric identities that you probably learned in previous years still apply to your calculus course... –  Guess who it is. Feb 8 '12 at 22:41
But you'll probably make your teacher happier if you put in some parentheses: $\int(\sin^2x+\cos^2x)\,dx=\int1\,dx$. –  Gerry Myerson Feb 8 '12 at 23:06

You don't even need to use any of the calculus you may have seen in the course, it just follows straight from the fact, that $\sin^2x + \cos^2x = 1$