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Chapter 4: Q. 4 (page 372)

Use a limit of Riemann sums to calculate the exact area under the graph of f(x)=x2on [0,5].

Short Answer

Expert verified

The area of the area under the graph f(x)=x2on the interval [0,5]is 41.6.

Step by step solution

01

Step 1. Given Information.

The function:

f(x)=x2 on the interval [0,5]

02

Step 2. Riemann integral formula.

The area can be estimated by,

A=鈭�abf(x).dx

03

Step 3. Substitute the values and find the area.

Substitute the known values in the above formula, we get,

A=鈭�05x2dx=[x33]50 =13(53-03)=1253鈮�41.6

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