How do you evaluate the definite integral #int (t^3-9t)dt# from [-1,1]?

1 Answer
Jan 31, 2017

#0.#

Explanation:

Observe that the Integrand #f(t)=t^3-9t, t in [-1,1],# is an odd
continuous function.

So, at a moment's glance, we can answer #0#, if we know the following Result :

# int_-a^af(t)dt=0, if f : [-a,a] to RR" is continuous & odd on "[-a,a].#

Alternatively, #int_-1^1(t^3-9t)dt=[t^4/4-(9t^2)/2]_-1^1#

#=[(1/4-9/2)-(1/4-9/2)]=0.#

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