Question

What is ∫−3x2+45x2−2x+1?

Answer 1

Here is your answer

- 82 is you answer

hope it help you dear

Answer 2

Using the fundamental theorem of calculus together with the chain rule, gives

f'(x) = exp[(x2 - 3x)2] d/dx (x2 - 3x) = (2x - 3)exp[(x2 - 3x)2]

The derivative is thus 0 at x = 3/2.

Taking the second derivative at x = 3/2 will determine if we have a minimum at that spot.

f''(x) = 2exp[(x2 - 3x)2] + (2x - 3)exp[(x2 - 3x)2]·2(x2 - 3x)(2x - 3)

= 2(4x4 - 24x3 + 45x2 - 27x + 1)exp[(x2 - 3x)2].

f''(3/2) = 2e81/16 > 0.

Thus f(x) has a minimum at x = 3/2.