Problem

Find the area under the curve $y=8 x^{4}$ over the interval $[0,5]$ Give the exact value.

Solution

Step 1 :The area under a curve y=f(x) from x=a to x=b is given by the definite integral of f(x) from a to b. In this case, we need to find the definite integral of \(8x^{4}\) from 0 to 5.

Step 2 :Let's denote x as x and f as \(8x^{4}\).

Step 3 :By calculating the definite integral, we find that the area under the curve is 5000.

Step 4 :\(\boxed{5000}\) is the exact value of the area under the curve \(y=8 x^{4}\) over the interval [0,5].

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Source: https://solvelyapp.com/problems/5Xdyb4yaPR/

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