The problem is asking for the integral of a linear combination of two functions, f(x) and g(x). The integral of a linear combination of functions is equal to the linear combination of their integrals. This is a property of integrals known as linearity.

Given that ∫10f(x) dx = 390 and ∫10g(x) dx = 160, we can find the integral of 10[4f(x) + 6g(x)] dx by using the linearity property.

First, distribute the 10 inside the brackets to get 40f(x) + 60g(x).

Then, separate the integral into two parts: ∫40f(x) dx + ∫60g(x) dx.

Since we know that ∫10f(x) dx = 390, we can find ∫40f(x) dx by multiplying both sides of the equation by 4 to get ∫40f(x) dx = 1560.

Similarly, since we know that ∫10g(x) dx = 160, we can find ∫60g(x) dx by multiplying both sides of the equation by 6 to get ∫60g(x) dx = 960.

Finally, add the two results together to find ∫10[4f(x) + 6g(x)] dx = 1560 + 960 = 2520.

Question

The problem is asking for the integral of a linear combination of two functions, f(x) and g(x). The integral of a linear combination of functions is equal to the linear combination of their integrals. This is a property of integrals known as linearity.

Given that ∫10f(x) dx = 390 and ∫10g(x) dx = 160, we can find the integral of 10[4f(x) + 6g(x)] dx by using the linearity property.

First, distribute the 10 inside the brackets to get 40f(x) + 60g(x).

Then, separate the integral into two parts: ∫40f(x) dx + ∫60g(x) dx.

Since we know that ∫10f(x) dx = 390, we can find ∫40f(x) dx by multiplying both sides of the equation by 4 to get ∫40f(x) dx = 1560.

Similarly, since we know that ∫10g(x) dx = 160, we can find ∫60g(x) dx by multiplying both sides of the equation by 6 to get ∫60g(x) dx = 960.

Finally, add the two results together to find ∫10[4f(x) + 6g(x)] dx = 1560 + 960 = 2520.

Knowee AI · Accepted Answer

The problem is asking for the integral of a linear combination of two functions, f(x) and g(x). The integral of a linear combination of functions is equal to the linear combination of their integrals. This is a property of integrals known as linearity.

Given that ∫10f(x) dx = 390 and ∫10g(x) dx = 160, we can find the integral of 10[4f(x) + 6g(x)] dx by using the linearity property.

First, distribute the 10 inside the brackets to get 40f(x) + 60g(x).

Then, separate the integral into two parts: ∫40f(x) dx + ∫60g(x) dx.

Since we know that ∫10f(x) dx = 390, we can find ∫40f(x) dx by multiplying both sides of the equation by 4 to get ∫40f(x) dx = 1560.

Similarly, since we know that ∫10g(x) dx = 160, we can find ∫60g(x) dx by multiplying both sides of the equation by 6 to get ∫60g(x) dx = 960.

Finally, add the two results together to find ∫10[4f(x) + 6g(x)] dx = 1560 + 960 = 2520.

If 10f(x) dx = 390 and 10g(x) dx = 16,0 find 10[4f(x) + 6g(x)] dx.0

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