If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let 
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that ![f^{-1}(x+1)=\sqrt[3]{x^2+2x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%2B1%29%3D%5Csqrt%5B3%5D%7Bx%5E2%2B2x%7D)
.
So, we can write the given integral as
Splitting up terms and replacing 
in the first integral, we get
The answer for 4 is 12..
hope it helps u..
have a great day ahead! :)
F(x)=3 domain: negative infinity, positive infinity range: 3
g(x)=x+7 domain: - infinity, + infinity range: - infinity, + infinity
P≈9.12
area 4
.......................................................................
Answer:
v = 66/7
Step-by-step explanation:
Step 1: Write equation
-7v + 3 = -63
Step 2: Solve for <em>v</em>
<u>Subtract 3 on both sides:</u> -7v = -66
<u>Divide both sides by -7:</u> v = 66/7
Step 3: Check
<em>Plug in x to verify if it's a solution.</em>
-7(66/7) + 3 = -63
-66 + 3 = -63
-63 = -63
