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

Worked solution for TMUA-P1-MM7-005 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM7-005 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM7-005 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM7-005?

No — calculators are banned in the TMUA. TMUA-P1-MM7-005 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-MM7-005?

TMUA-P1-MM7-005 is Paper P1 · Integration (specification code MM7), level 2. Drill more of the same topic from this page.

TMUA-P1-MM7-005 — Paper P1 · Integration · Level 2

P1MM7Level 2~180s target

Spec: MM7 · No calculator · ~180s

Given

\int_1^3 f(x)\,dx = 7

and

\int_1^5 f(x)\,dx = 4

, what is

\int_3^5 f(x)\,dx

Options

$11$
$-3$
$3$
$7$
$\dfrac{4}{7}$

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

Show solution

Split the range:

\int_1^5 = \int_1^3 + \int_3^5

, so

\int_3^5 = 4 - 7 = -3

. Trap:

11

adds the two integrals — plausible if you ignore that

[1,3]

is part of

[1,5]

, not separate.

Keep practising

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P1MM7Level 2
TMUA-P1-MM7-004
Suppose F'(x) = f(x) with F(5) = 20 and F(2) = 8. What is _2^5 f(x)\,dx?
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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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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: add-instead-of-subtract

P1MM7Level 2

TMUA-P1-MM7-004

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

Integration

Open TMUA-P1-MM7-004 →

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?

Integration

Open TMUA-P1-MM7-007 →

TMUA-P1-MM7-005 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration

TMUA-P1-MM7-005 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration