Maths question help. C2

(a) Write down the exact value of cos π6. (1)

The finite region R is bounded by the curve y = cos2 x, where x is measured in radians,the positive coordinate axes and the line x = π3.

(b) Use the trapezium rule with three equally-spaced ordinates to estimate the areaof R, giving your answer to 3 significant figures. (5)

The finite region S is bounded by the curve y = sin2 x, where x is measured in radians,the positive coordinate axes and the line x = π3.

(c) Using your answer to part (b), find an estimate for the area of S. (3)

Can someone explain how to work out 5b and 5c step by step.

Thanks in advance! :smile:

Reply 1

joostan

Original post by greentron6

What did you try?
This seems to be a fairly standard question using the Trapezium rule, you'll find a formula in your booklet.

Reply 2

greentron6

Original post by joostan

What did you try?
This seems to be a fairly standard question using the Trapezium rule, you'll find a formula in your booklet.

Hi again. My online Maths tutor! :biggrin:

I couldnt even attempt it, because i didn't know how to apply the width of the trapezium.

How would you solve b and c?

Reply 3

joostan

Original post by greentron6

Hi again. My online Maths tutor! :biggrin:

I couldnt even attempt it, because i didn't know how to apply the width of the trapezium.

How would you solve b and c?

Well based on what I'm guessing you meant from what you wrote, you want to approximate

\displaystyle\int_0^{\frac{\pi}{3}} \cos^2(x) \ dx

, with three ordinates.
It specifies that these should also be equally spaced.

Reply 4

greentron6

Original post by joostan

Well based on what I'm guessing you meant from what you wrote, you want to approximate

\displaystyle\int_0^{\frac{\pi}{3}} \cos^2(x) \ dx

, with three ordinates.
It specifies that these should also be equally spaced.

Yes, also will you intergrate sin2x in c?

Reply 5

joostan

Original post by greentron6

Yes, also will you intergrate sin2x in c?

There's no need to, you can use a well known trig identity and use the previous result.

Reply 6

greentron6

Thanks.

While you're hear, can you also explain to be b and c?

Amy plans to join a savings scheme in which she will pay in £500 at the start ofeach year.One scheme that she is considering pays 6% interest on the amount in the accountat the end of each year.
For this scheme,(a) find the amount of interest paid into the account at the end of the second year, (3)

(b) show that after interest is paid at the end of the eighth year, the amount in theaccount will be £5246 to the nearest pound. (4)

Another scheme that she is considering pays 0.5% interest on the amount in theaccount at the end of each month.
(c) Find, to the nearest pound, how much more or less will be in the account atthe end of the eighth year under this scheme.

Reply 7

joostan

Original post by greentron6

For b) I'd recommend writing down the amount of money at the end of the first couple of years - see if you can spot a pattern.

For c) Consider how the monthly interest affects a fixed sum after a whole year, and follow a similar line of argument to b).