Mishandling the constant of integration

The habit: Write + C every time, and fix each constant with the condition that belongs to that function.

8 practice questions are built to catch it, in 3 topics.

See it fail in a figure: Velocity to position, in the antiderivatives lesson

Practise against it: 6 questions

What it looks like

A question from antiderivatives, with the answer this slip gives beside the right one.

Introductory2 marks · 3 min

A function $F$ satisfies $F'(x) = 6x^{2} - 4x + 1$ and $F(0) = 2$ . Find $F(1)$ .

With the slip: $\displaystyle 1$
Worked through: $\displaystyle F(1) = 3$

2 − 2 + 1 = 1 leaves out C: use F(0) = 2 to find it, and add it in.

See the worked solution

Where it comes up

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
Which of the following functions satisfies the differential equation $\dfrac{dy}{dt} = 3y$ ?
Exponential growth and decayIntroductory
02
Which of the following is the most general antiderivative of $f(x) = 3\sin x - 2$ ?
AntiderivativesIntroductory
03
A function $f$ satisfies $f'(x) = 3$ for every real $x$ , and $f(1) = 2$ . Find $f(5)$ .
The Mean Value TheoremStandard
04
A ball is thrown straight up from a height of 1 m with an initial velocity of 14.7 m/s. Its acceleration is a constant $-9.8$ m/s². Find the maximum height it reaches.
AntiderivativesStandard
05
A function $F$ satisfies $F'(x) = 6x^{2}e^{x^{3}}$ and $F(0) = 0$ . Find $F(1)$ .
AntiderivativesChallenging
06
A function $f$ satisfies $f''(x) = 12x - 6$ , $f'(1) = 2$ and $f(0) = 5$ . Find $f(2)$ .
AntiderivativesChallenging