Chapter 5 Multiple choice questions

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. Which of the following is not true about integration?

It is the inverse of differentiation. correct incorrect

Unbounded integrals are only defined to within an arbitrary additive constant. correct incorrect

It relates to the area under a graph. correct incorrect

It can always be done analytically. correct incorrect

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. Given the velocity, v, of a car travelling along a straight road as a function of time, t, which of the following is not related to v(t) through integration?

The acceleration. correct incorrect

The average velocity. correct incorrect

The average speed (|v|). correct incorrect

The distance travelled. correct incorrect

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. What is the average value of sin²(x) between x=0 and x=2π?

0 correct incorrect

1/2 correct incorrect

2/π correct incorrect

1 correct incorrect

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. If J_n is defined to be the integral of xⁿ e^-x between zero and infinity, then an integration by parts leads to the reduction formula J_n = n J_n-1 for n≥1. If n is a positive integer, what is the value of J_n?

n² correct incorrect

n^n-1 correct incorrect

n! correct incorrect

eⁿ correct incorrect

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. What is the integral of exp(-x²) ?

exp(-x²) + K correct incorrect

-2x exp(-x²) + K correct incorrect

exp(-x²) / (-2x) + K correct incorrect

It has to be computed numerically for arbitrary limits, and is often tabulated in formulae books. correct incorrect