Content
Access custom-built, exam-style problems for integration. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Ask Plex AI about problem 3
Get hints, ask questions, and work through this problem step by step
Select a Difficulty:
9 / 21 problems visible - Upgrade to view all problems
!
0 / 5
Consider a function f whose derivative is
Find an expression for f(x).
Given that f(1)=4, determine C.
Write down, without evaluation, the definite integral that gives the area A under the curve y=f(x) between x=0 and x=2.
Evaluate this integral to find the exact value of A.
!
0 / 6
BrightBike manufactures electric bicycles. The marginal cost (in $USD per bike) when producing x bikes is
and the total cost at zero production is $100.
Find an expression for the total cost C(x).
It is given that C(0)=100.
Determine the constant C and write down the particular C(x).
Write down, without evaluation, the definite integral that gives the accumulated cost of producing the first 20 bikes.
Evaluate the integral to find the exact total cost of producing 20 bikes.
!
0 / 4
Consider the population P(t) of island mice, where t is measured in years. The rate of change of the population is modeled by
and initially P(0)=50.
Find P(t).
Write down, without evaluation, the definite integral giving the total “mouse‑years” lived from t=1 to t=4.
Evaluate the integral found in part (b).
!
0 / 4
!
0 / 5
!
0 / 5
!
0 / 4
!
0 / 9
!
0 / 10