Durham College · MATH 3132

Durham MATH 3132 tutoring

Help with derivatives, integrals, motion, areas and volumes in Durham MATH 3132.

Online 60 min: $55 CAD · Pricing Midterm & final exam help Compare displacement with distance travelled Free study guide for MATH 3132

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Course overview

MATH 3132 combines differential and integral calculus in Durham’s Mechanical Engineering Technology curriculum. Rates, motion, areas and volumes connect symbolic techniques to physical quantities. In motion problems, integrating velocity gives signed displacement; finding distance travelled may require splitting the interval where direction changes. Continuing students should use their own intake-year program of study.

MATH 3132 topics to review

Derivatives, rates and motionDefinite integration and accumulationAreas and volumes

Common difficulties

Treating a signed integral as total distance
Missing a direction change inside the interval

Preparing for this course

Review factoring polynomials and determining their signs on intervals. To interpret a velocity integral, mark its zeros on a time line first. Use the graph to predict cancellation before calculating; a zero displacement does not necessarily mean the object stayed still.

Registration requirements

The guidance above is study preparation, not an eligibility decision. Confirm current prerequisites, restrictions and availability with Durham College.

Check the official course catalogue

Distinguish displacement from distance

An object has velocity $v(t)=3t^2-6t$ m/s for $0\le t\le3$ , with $t$ in seconds. Find displacement and total distance travelled.

Show the reasoning

Locate the change of direction
Factor $v(t)=3t(t-2)$ . It is negative on $(0,2)$ and positive on $(2,3)$ , so the object reverses direction at 2 s.
Integrate the signed velocity
An antiderivative is $F(t)=t^3-3t^2$ . Displacement is $F(3)-F(0)=0\text{ m}$ . The object ends where it started.
Add the lengths of both parts
The first displacement is $F(2)-F(0)=-4\text{ m}$ ; the second is $F(3)-F(2)=4\text{ m}$ . Distance is $|-4|+|4|=8\text{ m}$ . Taking the absolute value only after combining the integrals would lose the journey.

Try a changed problem

Over $0\le t\le2$ , what are displacement and distance?

Check your reasoning

Displacement is −4 m and distance is 4 m. There is no reversal inside this shorter interval, so one sign applies throughout its interior.

How tutoring can help

Share a derivative or integral question, even if you are unsure of the first step. For integration, a tutor can help you identify the accumulated quantity, sketch the situation and choose the bounds. We can work through sign changes together, then explore how a shorter interval changes the answer.

Exam preparation for MATH 3132

Practise both derivative applications and definite integrals from the chapters announced for your assessment. Label all quantities and units, and distinguish signed results from nonnegative geometric quantities. Explain why an interval must be split before adding its pieces.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Independent practice

Free practice and study guides for MATH 3132

35 min

How to Choose an Integration Method

Compare substitution, integration by parts, partial fractions and trigonometric substitution, with sign-aware radical choices, worked examples and progressive checks.

40 min

Motion Graphs: From the Story to the Equation

Translate a motion story into position, velocity and acceleration graphs. Read slopes and signed areas, choose valid kinematics equations, and try six explained questions.

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MATH 3132 · official course reference