Help!! I spent hours trying to figure this out!! Answer was incorrect. And it has to be written in equation or fraction format.
No decimals.
Here’s my work:
Using a substitution
u = 4 * x^(-2)
du = -8 * x^(-3) * dx
(-1/8) * du = x^(-3) * dx
Now I have:
e^(4x^(-2)) * dx / x^3 =>
e^(u) * (-1/8) * du
Integrate
(-1/8) * e^(u) + C =>
(-1/8) * e^(4x^(-2)) + C
From 4 to 6
(-1/8) * e^(4 * 6^(-2)) + (1/8) * e^(4 * 4^(-2)) =>
(1/8) * (e^(4/16) - e^(4/36)) =>
(1/8) * (e^(1/4) - e^(1/9))
Here’s my work:
Using a substitution
u = 4 * x^(-2)
du = -8 * x^(-3) * dx
(-1/8) * du = x^(-3) * dx
Now I have:
e^(4x^(-2)) * dx / x^3 =>
e^(u) * (-1/8) * du
Integrate
(-1/8) * e^(u) + C =>
(-1/8) * e^(4x^(-2)) + C
From 4 to 6
(-1/8) * e^(4 * 6^(-2)) + (1/8) * e^(4 * 4^(-2)) =>
(1/8) * (e^(4/16) - e^(4/36)) =>
(1/8) * (e^(1/4) - e^(1/9))
1 answer:
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Answer:
Rate of change of the area of the square is 42 units at t = 2.
Step-by-step explanation:
We note that the area of the square is given by: but we aim to find
. But we can use the chain rule to pull out that dA/dt. Doing so gives us:
Now, (by the power rule and
But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.
So, finally, we see that: