Could someone help me out?

Question

Students must attend t hours, where t ∈ [0,H], of lectures. The number of students who attended between t₁ and t₂ hours of lectures is described by the integral

t₁

∫ 20t² dt,             0 ≤ t₁ < t₂ ≤ H.

t₂

(a) some students attended less than H/2 hours of lectures. Find the ratio of students who attended less than H/2 hours of lectures.

(B) The final score each student got is proportional to the amount of lectures he/she had attended which is given by the function

L(t) = (100/H)t

What was the average score in the class?

Answer 1

Students must attend t hours, where t ∈ [0,H], of lectures. The number of students who attended between t₁ and t₂ hours of lectures is described by the integral

t₁

∫ 20t² dt,             0 ≤ t₁ < t₂ ≤ H.

t₂

t₁

∫ 20t² dt,    = 20/3( t₁ ³ -t₂ ³  )   0 ≤ t₁ < t₂ ≤ H.

t₂

In first case Limit of t is 0 to H/2 and others H/2 to H

A1 = 20/3( H/2)³

A2 = 20/3 [H³- (H/2)³ ]