8.3 Using Accumulation functions and Definite integrals in Applied Problems

8.3 Using Accumulation functions and Definite integrals in Applied Problems

Objective:• Interpret the meaning of a definite integral in

accumulation problem.

• Determine net change using definite integral in applied context.

Vocabs:Rate of change

Definite Integral

Accumulation function

Area under the graph

Definite Integral:

𝐴𝑟𝑒𝑎 = න𝑎

𝑏

𝑓 𝑥 𝑑𝑥

න𝑎

𝑏

𝑓 𝑥 𝑑𝑥 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎 < 𝑡 < 𝑏.

𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 + න𝑎

𝑏

𝑓 𝑥 𝑑𝑥

Note: 𝑝 𝑡 = ′𝑝 𝑡 𝑑𝑡