Rahul evaluated as

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

Problem

Rahul evaluated

\int_0^2 (x^2+1)\,dx

\left(\dfrac{x^3}{3}+x+C\right)_0^2 = \dfrac{8}{3}+2+C

. Which of the following best explains the error in his solution? (a) He misapplied the power rule; the antiderivative of

x^{2}

x^{3}/2

, not

x^{3}/3

, so the numerical result is wrong. (b) He included the constant of integration in a definite integral; writing “

+C

” produced the extra term. (c) He omitted the substitution of the lower limit; for a definite integral one must compute

F(2)-F(0)

. (d) He actually differentiated

(x^{2}+1)

instead of integrating it, which led to the form

\dfrac{x^{3}}{3}+x