A student evaluates and concludes that the antiderivative is

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A student evaluates

\displaystyle \int 5x^{3}\,dx

and concludes that the antiderivative is

\dfrac{x^{4}}{4}+C

. Which statement best describes the student’s error? (a) The power rule was applied incorrectly; after integration the exponent should be

5

, not

4

. (b) The coefficient should be

5

with no denominator of

4

, giving

5x^{4}+C

. (c) The factor

5

should remain after integration, so the result should be

\dfrac{5x^{4}}{4}+C

. (d) The student confused integration with differentiation; the exponent should decrease to

2

, yielding

\dfrac{5x^{2}}{2}+C