College Math Placement Practice Test

Question: 1 / 400

What is the result of evaluating the integral ∫(2x)dx?

x + C

x² + C

To evaluate the integral ∫(2x)dx, we apply the power rule for integration. The power rule states that the integral of x raised to the power n is (x^(n+1))/(n+1) plus a constant of integration, C.

In the case of the integrand 2x, we can consider this as 2 times x raised to the power of 1. According to the power rule:

1. Increase the exponent by one: from 1 to 2.

2. Divide by the new exponent: divide by 2.

So, the integral can be computed as follows:

∫(2x)dx = 2 * (x^(1+1))/(1+1) + C

= 2 * (x²/2) + C

= x² + C.

Thus, when you perform the integration correctly, you arrive at x² + C, which confirms that this option is indeed the correct result for the integral ∫(2x)dx. The constant C represents any constant value that could be added because the integral represents an entire family of functions.

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2x² + C

3x² + C

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