Figure 1 below shows the region $R$ , which is bounded by the curve with equation $\sqrt{2^x + 1}$ , the $x$ -axis and the lines $x = 0$ and $x = 3$ .

Figure for question 7

Complete the table below, giving the missing values of $\sqrt{2^x + 1}\,$ to three decimal places.

$x$ : 0, 0.5, 1, 1.5, 2, 2.5, 3 $2x+1\sqrt{2^x + 1}$ : 1.414, 1.554, 1.732, 1.957, ..., ..., ...

Use the trapezium rule with all the values from the table to find an approximation for the area of $R$ , giving your answer to four significant figures.

State, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of $R$ .

Figure 1 below shows the region $R$ , which is bounded by the curve with equation $\sqrt{2^x + 1}$ , the $x$ -axis and the lines $x = 0$ and $x = 3$ .

Figure for question 7

Complete the table below, giving the missing values of $\sqrt{2^x + 1}\,$ to three decimal places.

$x$ : 0, 0.5, 1, 1.5, 2, 2.5, 3 $2x+1\sqrt{2^x + 1}$ : 1.414, 1.554, 1.732, 1.957, ..., ..., ...

Use the trapezium rule with all the values from the table to find an approximation for the area of $R$ , giving your answer to four significant figures.

State, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of $R$ .

1 Pure Mathematics

Question 458

Markscheme

1 Pure Mathematics

Question 458

Markscheme

1 Pure Mathematics

Question 458

1 Pure Mathematics Questions

1 Pure Mathematics

Question 458

1 Pure Mathematics Questions