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Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesMatricesComplex NumbersFinancial Mathematics
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
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DifferentiationIntegrationDifferential Equations
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Perplex
IB Math AIHL
/
Integration
/
Problem Bank
IB Math AIHL
/
Integration
/
Problem Bank

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[Maximum mark: 4]

On a rainy afternoon, the community reservoir at Brookview Park begins to fill. Let ​V(t)​ (in m³) be the volume of water in the reservoir ​t​ minutes after the rain starts. Engineers have determined that the fill‑rate varies according to

​
dtdV​=t2−2t,t≥0,
​

and at ​t=2​ minutes the reservoir holds ​10m3.

  1. Give an expression for ​V(t).

    [2]
    Part (a):
    V(t)=
  2. Determine how many cubic meters of water are added to the reservoir between ​t=2 min​ and ​t=5 min.

    [2]
[Maximum mark: 4]

On a rainy afternoon, the community reservoir at Brookview Park begins to fill. Let ​V(t)​ (in m³) be the volume of water in the reservoir ​t​ minutes after the rain starts. Engineers have determined that the fill‑rate varies according to

​
dtdV​=t2−2t,t≥0,
​

and at ​t=2​ minutes the reservoir holds ​10m3.

  1. Give an expression for ​V(t).

    [2]
    Part (a):
    V(t)=
  2. Determine how many cubic meters of water are added to the reservoir between ​t=2 min​ and ​t=5 min.

    [2]