Is a number between?

Question

If f(x)=8-x^2 for -2≤x≤2, f(x)=x^2 elsewhere, then ∫ f(x) dx from -1 to 3 is a number between?

 

a) 0 and 8

b) 8 and 16

c) 16 and 24

d) 24 and 32

e) 32 and 40

 

Answer: D

Answer 1

∫_-1³ f(x) dx = ∫_-1² (8-x²) dx + ∫₂³ x² dx = [8x - x³/3] _-1² + [x³/3]₂³ = 65/3 + 19/3 = 84/3 = 28

 

Answer: D