Evaluate the integral [0,10] f(x)dx

Question

Evaluate the integral [0,10] f(x)dx

8x, x<=5

f(x)= and

9/x x>5

Answer 1

∫₀⁵8 xdx + ∫₅¹⁰ (9/x)dx = 4(25 -0) + 9ln10 -9ln5 = 100 + 9 ln 10/5 =100 +9ln2

Answer 2

Hi Mindy,

1) Integrate 8x from 0 to 5:

∫₀⁵ 8x dx

= 4x² |₀⁵

= 4(5)² - 4(0)²

= 4(25)

= 100

2) Integrate 9/x from 5 to 10:

∫₅¹⁰ 9/x dx

= 9 ∫ 1/x dx

= 9 (ln(x) |₅¹⁰)

= 9 (ln(10) - ln(5))

= 9 (ln (10/5))

= 9ln(2)

3) Add:

∫₀⁵ 8x dx + ∫₅¹⁰ 9/x dx

= 100 + 9ln(2)