Suppose F'(x) = f(x) with F(5) = 20 and F(2) = 8. What is _2^5 f(x)\,dx?

Worked solution for TMUA-P1-MM7-004 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM7-004 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM7-004 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM7-004?

No — calculators are banned in the TMUA. TMUA-P1-MM7-004 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM7-004?

TMUA-P1-MM7-004 is Paper P1 · Integration (specification code MM7), level 2. Drill more of the same topic from this page.

TMUA-P1-MM7-004 — Paper P1 · Integration · Level 2

P1MM7Level 2~180s target

Spec: MM7 · No calculator · ~180s

Suppose

F'(x) = f(x)

with

F(5) = 20

and

F(2) = 8

. What is

\int_2^5 f(x)\,dx

Options

$28$
$20$
$12$
$8$
$4$

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: FTC, add-instead-of-subtract. Name the trap first, work the stem by hand, then open the solution below.

Show solution

By the fundamental theorem,

\int_2^5 f = F(5) - F(2) = 20 - 8 = 12

. Trap:

28

adds the endpoint values — plausible if you confuse

F(b) - F(a)

with

F(b) + F(a)

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Same topic · same level

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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…

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Open TMUA-P1-MM7-003 →

Same trap: add-instead-of-subtract

P1MM7Level 2

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Given _1^3 f(x)\,dx = 7 and _1^5 f(x)\,dx = 4, what is _3^5 f(x)\,dx?

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Open TMUA-P1-MM7-005 →

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-MM7-004 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration

TMUA-P1-MM7-004 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration