Theory question 102
IntegrationEvaluate: ∫19 x(2x − 3)/√x dx
Show the model answer
Model answer
x(2x − 3)/√x = 2x^(3/2) − 3x^(1/2).
∫ = [4x^(5/2)/5 − 2x^(3/2)] from 1 to 9.
At 9: 4(243)/5 − 54 = 140.4. At 1: 4/5 − 2 = −1.2.
Answer = 141.6 (= 708/5).
Explanation
Split the fraction into powers of x first.