Evaluate
2\sin(45)\sin(55)\approx -1.701390401
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\int \sin(t)\mathrm{d}t
Evaluate the indefinite integral first.
-\cos(t)
Use \int \sin(t)\mathrm{d}t=-\cos(t) from the table of common integrals to obtain the result.
-\cos(100)+\cos(-10)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
2\sin(55)\sin(45)
Simplify.
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