tmua 2022 Q12

tmua · Uk · paper2 1 marks Indefinite & Definite Integrals Integral Inequalities and Limit of Integral Sequences

Place the following integrals in order of size, starting with the smallest.
$$\begin{aligned} & P = \int _ { 0 } ^ { 1 } 2 ^ { \sqrt { x } } \mathrm {~d} x \\ & Q = \int _ { 0 } ^ { 1 } 2 ^ { x } \mathrm {~d} x \\ & R = \int _ { 0 } ^ { 1 } ( \sqrt { 2 } ) ^ { x } \mathrm {~d} x \end{aligned}$$
A $P < Q < R$
B $P < R < Q$
C $Q < P < R$
D $Q < R < P$
E $\quad R < P < Q$ F $R < Q < P$

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Place the following integrals in order of size, starting with the smallest.

$$\begin{aligned}
& P = \int _ { 0 } ^ { 1 } 2 ^ { \sqrt { x } } \mathrm {~d} x \\
& Q = \int _ { 0 } ^ { 1 } 2 ^ { x } \mathrm {~d} x \\
& R = \int _ { 0 } ^ { 1 } ( \sqrt { 2 } ) ^ { x } \mathrm {~d} x
\end{aligned}$$

A $P < Q < R$\\
B $P < R < Q$\\
C $Q < P < R$\\
D $Q < R < P$\\
E $\quad R < P < Q$\\
F $R < Q < P$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20