Question

Evaluate the following definite integrals: `int_4^9 (1)/sqrt(x)*dx`

Answer 1

Let I = `int_4^9 (1)/sqrt(x)*dx`

= `int_4^9x^(1/2)*dx = [(x^(1/2))/(1/2)]_4^9`

= `2[sqrt(x)]_4^9`

= `2(sqrt(9) - sqrt(4))`

= 2 (3 – 2)
∴ I = 2.