Applications

Suppose that f(x) = d/dx (1 − √x...

Question

Applications

Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).

Find:

∫[−f(x)] dx

Accepted Answer

Welcome back everyone. Let f x be equal to d divided by dx of 3 minus x to the power of 3 halves. Compute the integral of fx dx. A says x to the power of 3 halves plus c. B g x to the power of 3 halves plus c. C 3 halves x, the power of 3 halves plus c, and D 1/2 x the power of 3 halves plus c. So for this problem, we want to evaluate the integral of negative, F of XDX. Let's remember that using the properties of integrals we can factor out the negative sign, and this is going to be a negative integral of F of XD X. And we're going to replace F of X with its actual expression, which gives us negative integral. Of d divided by dx of 3 minus x is the power of 3 halves d x. Now notice that we can cancel out the differential dx. Which gives us negative integral of d of 3 minus x the power of 3 halves. Let's remember that the integral of d x is simply equal to x plus some constant of integration C1. So in this case, we are going to get negative of. 3 minus x to the power of 3 halves. Plus some constant of integration c1. Distributing the negative sign, we are going to get -3. Plus x to the power of 3 halves plus c1 and what we can do is simply combine the two constants -3 plus c1 can be labeled with c. So the final answer is going to be x to the power of 3 halves plus c, which corresponds to the answer choice a. Thank you for watching.

ApplicationsSuppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).Find:∫[−f(x)] dx

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Applications

Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).

Find:

∫[−f(x)] dx