Question

Calculate the following antiderivatives:

(a) ∫3xdx = [insert answer here] +C.
A) 3/2x² + C
B) x³ + C
C) 3x + C
D) 6x + C

Answer 1

The antiderivative of 3x is 3/2x² + C.

Step-by-step explanation:

To calculate the antiderivative of 3x, we can use the power rule of integration. The power rule states that the antiderivative of xⁿ is (1/(n+1)) * xⁿ⁺¹ + C, where C is the constant of integration. Applying this rule to our problem, we have:

∫3xdx = (1/2) * x² + C

Hence, the accurate answer corresponds to A) 3/2x² + C, showcasing how the application of the power rule in integration enables the derivation of antiderivatives, providing a comprehensive method to find the reverse process of differentiation for various functions.