If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a ≤ M(b − a). Use this property to estimate the value of the integral. 1 0 x3 dx

m = 1.5

M = 3

Step-by-step explanation:

According to the situation, the solution is as follows

Here we need to determine the maximum and minimum of

Now we have to differentiate it

Now the points i.e x = 0 and x =1 could be tested

= 3

= 1.5

So,

m = 1.5

M = 3

By applying the differentiation we could easily estimate the value of the integral and the same is to be shown above