Find the exact value of each definite integral or indefinite

Find the exact value of each definite integral or indefinite integral. Please show steps very lost.

Solution

let sin x = t

So, cosx dx = dt

So, we have,

integration of t³ dt

= t⁴/4

= (sinx)⁴/4 from pi/6 to pi/2

= ((1)⁴ -0.5⁴)/4= 0.234375