Values of f at x = 0, 1, 2, 3 are 2, 5, 6, 9. What is the trapezium-rule estimate of _0^3 f(x)\,dx with 3 strips?

Worked solution for TMUA-P1-MM7-006 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM7-006 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM7-006 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM7-006?

No — calculators are banned in the TMUA. TMUA-P1-MM7-006 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM7-006?

TMUA-P1-MM7-006 is Paper P1 · Integration (specification code MM7), level 2. Drill more of the same topic from this page.

TMUA-P1-MM7-006 — Paper P1 · Integration · Level 2

P1MM7Level 2~210s target

Spec: MM7 · No calculator · ~210s

Values of

f

x = 0, 1, 2, 3

are

2, 5, 6, 9

. What is the trapezium-rule estimate of

\int_0^3 f(x)\,dx

with

3

strips?

Options

$33$
$22$
$16$
$20$
$\dfrac{33}{2}$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: trapezium-rule, missing-half. Name the trap first, work the stem by hand, then open the solution below.

Show solution

With

h = 1

: estimate

= \frac{1}{2}(2 + 9 + 2(5 + 6)) = \frac{33}{2}

. Trap:

33

forgets the outer

\frac{1}{2}

— plausible as it is the bracket total.

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Keep practising

Same topic · same level

P1MM7Level 2

TMUA-P1-MM7-003

The curve y = 2x - 6 lies below the x -axis between x = 1 and x = 3. What is the area enclosed by the curve, the x -axis…

Integration

Open TMUA-P1-MM7-003 →

Same trap: missing-half

P1MM4Level 2

TMUA-P1-MM4-008

A sector of a circle of radius 4 has angle 3π/4 radians. What is its area?

Trigonometry

Open TMUA-P1-MM4-008 →

Step up a level

P1MM7Level 3

TMUA-P1-MM7-007

A curve satisfies dy/dx = 6x^2 - 4x + 1 and passes through (1, 3). What is its equation?

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Open TMUA-P1-MM7-007 →

TMUA-P1-MM7-006 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration

TMUA-P1-MM7-006 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration