find-the-average-value-of-the-function-on-the-given-interval-gt-dfractsqrt3-t2-1-3

Question

Find the average value of the function on the given interval.

$ g(t) = \dfrac{t}{\sqrt{3 + t^2}} $ , $ [1, 3] $

Amrita Bhasin · Accepted Answer

we know we&#x27;re using the average value formula, which is one over B, which is three minus a, which is one from the bounds of 80 B or 123 or function T over three plus t squared square rooted D T. We know we can simplify this to be 1/4 times two and then we know we should actually do U substitution over here. So let&#x27;s define our you is three plus t squared. Therefore, our do your derivative is to t d t right Because the three cancels, it&#x27;s just a constant. Therefore, we have two year the 1/2 from 4 to 12 plugging in 1/2 time squirt of 12 minus squared of four gives us sward of three minus one. This is also known as 0.732 if you prefer in the decibel form.

Problem

Find the average value of the function on the giv…

Problem 4 Medium Difficulty

Find the average value of the function on the given interval.

$ g(t) = \dfrac{t}{\sqrt{3 + t^2}} $ , $ [1, 3] $

Answer

$\sqrt{3}-1 \approx 0.732$

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