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Grade 11Integral Calculus

Plz help me out in this definite integration
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Question image for Plz help me out in this definite integration Plzz

Chintan Shah

7 Years agoGrade 11

1 Answer

Aditya Gupta

Approved Tutor Answer7 Years ago

the answer will be n – 1.

here, we will use the formula ∫0 to n*T f(x)dx = n*∫0 to T f(x)dx where T is the period of the function and n is an integer.

now note that f(x)= {x} is a periodic function with period T= 1. so ∫0 to n {x}dx = n*∫0 to 1 {x}dx= n*∫0 to 1 xdx (as between 0 to 1 {x}= x)= n*x^2/2= n*1/2= n/2

now write ∫0 to n [x]dx= ∫0 to n xdx – ∫0 to n {x}dx= x^2/2 – n/2= n^2/2 – n/2

now divide the two (n^2/2 – n/2)/(n/2)

= n – 1.

kindly approve :)

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