The question seems to be incomplete. The integral ∫20f(x)dx is missing the limits of integration. If you want to integrate from 0 to 2, it should be written as ∫ from 0 to 2 of 20f(x)dx.

Assuming that's what you meant, here's how you would solve it:

1. First, note that the constant 20 can be factored out of the integral, so ∫ from 0 to 2 of 20f(x)dx = 20 * ∫ from 0 to 2 of f(x)dx.

2. To evaluate the integral ∫ from 0 to 2 of f(x)dx, you would need to know the antiderivative F(x) of f(x), such that F'(x) = f(x).

3. Once you have F(x), you can use the Fundamental Theorem of Calculus, which states that ∫ from a to b of f(x)dx = F(b) - F(a).

4. So, ∫ from 0 to 2 of f(x)dx = F(2) - F(0).

5. Therefore, ∫ from 0 to 2 of 20f(x)dx = 20 * (F(2) - F(0)).

Without knowing the specific function f(x), this is as far as we can go.

Question

The question seems to be incomplete. The integral ∫20f(x)dx is missing the limits of integration. If you want to integrate from 0 to 2, it should be written as ∫ from 0 to 2 of 20f(x)dx.

Assuming that's what you meant, here's how you would solve it:

1. First, note that the constant 20 can be factored out of the integral, so ∫ from 0 to 2 of 20f(x)dx = 20 * ∫ from 0 to 2 of f(x)dx.

2. To evaluate the integral ∫ from 0 to 2 of f(x)dx, you would need to know the antiderivative F(x) of f(x), such that F'(x) = f(x).

3. Once you have F(x), you can use the Fundamental Theorem of Calculus, which states that ∫ from a to b of f(x)dx = F(b) - F(a).

4. So, ∫ from 0 to 2 of f(x)dx = F(2) - F(0).

5. Therefore, ∫ from 0 to 2 of 20f(x)dx = 20 * (F(2) - F(0)).

Without knowing the specific function f(x), this is as far as we can go.

Knowee AI · Accepted Answer

The question seems to be incomplete. The integral ∫20f(x)dx is missing the limits of integration. If you want to integrate from 0 to 2, it should be written as ∫ from 0 to 2 of 20f(x)dx.

Assuming that's what you meant, here's how you would solve it:

1. First, note that the constant 20 can be factored out of the integral, so ∫ from 0 to 2 of 20f(x)dx = 20 * ∫ from 0 to 2 of f(x)dx.

2. To evaluate the integral ∫ from 0 to 2 of f(x)dx, you would need to know the antiderivative F(x) of f(x), such that F'(x) = f(x).

3. Once you have F(x), you can use the Fundamental Theorem of Calculus, which states that ∫ from a to b of f(x)dx = F(b) - F(a).

4. So, ∫ from 0 to 2 of f(x)dx = F(2) - F(0).

5. Therefore, ∫ from 0 to 2 of 20f(x)dx = 20 * (F(2) - F(0)).

Without knowing the specific function f(x), this is as far as we can go.

Let f(x) be a differentiable function in the interval (0,2), then the value of ∫20f(x)dx

Question

Let f(x) be a differentiable function in the interval (0,2), then the value of $\int_{2}^{0} f(x) \, dx$

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