Let f be a differentiable function such that f(1)=π2 and f′(x)=3arctan(x2−3x+2). What is the value of f(3) ?

2.899

Step-by-step explanation:

Given that:

x     1      1.2      1.4      1.6      1.8      2      2.2      2.4      2.6      2.8      3

y   f(0)  f(1.2)   f(1.4)   f(1.6)   f(1.8)   f(2.0)  f(2.2)  f(2.4)  f(2.6)  f(2.8)   f(3)

By simpson's rule:

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.