If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, fin...

Question

If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, find the value of each of the following.

b. ∫₁² g(x) dx

Accepted Answer

Welcome back everyone. Suppose integral from 0 to 3 of 2 f xdx is equal to 6 and integral from 0 to 1 of f xDX is equal to 1. Find integral from 1 to 3 of fxdx. A negative1, B1, C2, and D 3. For this problem, we're going to use the properties of integrals. We want to identify the integral from 1 up to 3 of F of X D X. Now let's remember one of the main properties of integrals. Since one of our integrals is integral from 0 to 3, let's simply express the integral from 0 to 3 of F of XDX as a sum of two integrals. So for the first integral, we can take the integral from 0 to 1, similar to the integral that we have in the problem. So that'd be integral from 0 to 1 of F of X D X plus. Now for the second integral, we start at 1 because this was the upper limit of integration for the first integral. So that'd be the integral from 1 up to the final limit of integration 3 of F of X D X. From this expression we can show that the integral from 1 to 3 of f of x dx is simply equal to the integral from 0 to 3 of fx dx minus. The integral from 0 to 1. Of F of X D X Now, what do we know? Well, essentially we know the value of the integral from 0 to 1 of F of XDX. It is equal to 1. So all that we have to do is identify the integral from 0 to 3 of F of XDX. Knowing that the integral of 2 f of x dx from 0 to 3 is equal to 6. And what we can do is simply factor out the constant using another property of integrals. So 2 integral from 0 to 3 of fx dx is going to be equal to 6. And then we can divide both sides by 2, right? So we can cross out 2 on the left-hand side, and 6 divided by 2 gives us 3. So now we know the next value, the integral from 0 to 3 of F of XDX is equal to 3. And finally we get 3 minus 1. Which is equal to 2, so the final answer corresponds to the answer choice c. Thank you for watching.

If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, find the value of each of the following.b. ∫₁² g(x) dx

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If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, find the value of each of the following.

b. ∫₁² g(x) dx