A-Level Edexcel Maths Pure Geometric Sequences & Series: y = \sqrt{3 + x} (a) Complete t

y = \sqrt{3 + x} (a) Complete the table below, giving the values of y to 3 decimal places - Edexcel - A-Level Maths Pure - Question 9 - 2012 - Paper 3

Question 9

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y = \sqrt{3 + x} (a) Complete the table below, giving the values of y to 3 decimal places. | x | 0 | 0.25 | 0.5 | 0.75 | 1 | |-----|------|-------|----... show full transcript

Worked Solution & Example Answer:y = \sqrt{3 + x} (a) Complete the table below, giving the values of y to 3 decimal places - Edexcel - A-Level Maths Pure - Question 9 - 2012 - Paper 3

Step 1

(a) Complete the table below, giving the values of y to 3 decimal places.

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Answer

To complete the table, we calculate the values of y using the function:

For x = 0:

y = \sqrt{3 + 0} = \sqrt{3} \approx 1.000

For x = 0.25:

y = \sqrt{3 + 0.25} = \sqrt{3.25} \approx 1.251

For x = 0.5:

y = \sqrt{3 + 0.5} = \sqrt{3.5} \approx 1.495

For x = 0.75:

y = \sqrt{3 + 0.75} = \sqrt{3.75} \approx 1.936

For x = 1:

y = \sqrt{3 + 1} = \sqrt{4} = 2.000

The final table will be:

x	0	0.25	0.5	0.75	1
y	1	1.251	1.495	1.936	2

Step 2

(b) Use the trapezium rule with all the values of y from your table to find an approximation for the value of \int_0^1 \sqrt{3 + x} \, dx

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Answer

To apply the trapezium rule, we use the formula:

$I \approx \frac{h}{2} (y_0 + 2y_1 + 2y_2 + 2y_3 + y_n)$

Where:

h is the width of each interval.
y_0, y_1, y_2, y_3, and y_n are the values of y from the table.

Here, the interval from 0 to 1 is divided into 4 parts:
- h = (1 - 0) / 4 = 0.25
Plugging in values into the formula:

$I \approx \frac{0.25}{2} (1 + 2(1.251) + 2(1.495) + 2(1.936) + 2)$

$= 0.125 (1 + 2.502 + 2.990 + 3.872 + 2)$

$= 0.125 (12.364) \approx 1.5455$

Therefore, the approximation for the value of \int_0^1 \sqrt{3 + x} , dx \approx 1.5455.

y = \sqrt{3 + x} (a) Complete the table below, giving the values of y to 3 decimal places - Edexcel - A-Level Maths Pure - Question 9 - 2012 - Paper 3

Worked Solution & Example Answer:y = \sqrt{3 + x} (a) Complete the table below, giving the values of y to 3 decimal places - Edexcel - A-Level Maths Pure - Question 9 - 2012 - Paper 3

(a) Complete the table below, giving the values of y to 3 decimal places.

(b) Use the trapezium rule with all the values of y from your table to find an approximation for the value of \int_0^1 \sqrt{3 + x} \, dx

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