Suppose Evaluate the following i have no idea what to do here, any help and explanations would be very helpful.
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It's just a substitution! Put $\displaystyle u=\frac t6\implies du=\frac{dt}6$ and you'll get $\displaystyle 0\le u\le6$ so your integral becomes $\displaystyle 6\int_0^6g(u)\,du=6\times6=36.$
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