Apentix/AP Calculus AB/Unit 6: Integration and Accumulation of Change/Question
AP Calculus ABeasymcq1 pt

Which of the following equals ∫(2x3−3x2+4) dx\int (2x^3-3x^2+4)\,dx?

A.x42−x3+4x+C\frac{x^4}{2}-x^3+4x+C
B.x42−x3+4x\frac{x^4}{2}-x^3+4x
C.6x2−6x+C6x^2-6x+C
D.x42−x3+C\frac{x^4}{2}-x^3+C

Explanation

Core Concept

Integrate term by term: 2x3→x4/22x^3\to x^4/2, −3x2→−x3-3x^2\to -x^3, and 4→4x4\to 4x. The result is x4/2−x3+4x+Cx^4/2-x^3+4x+C.

Correct Answer

Ax42−x3+4x+C\frac{x^4}{2}-x^3+4x+C

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