Home
Class 12
MATHS
Evaluate: int(x^3)/((x-1)(x-2))dx...

Evaluate: `int(x^3)/((x-1)(x-2))dx`

A

a positive integer

B

divisible by n

C

equal to `n + (1)/(n)`

D

never less than n

Text Solution

Verified by Experts

The correct Answer is:
D
Since, product of n positive numbers is unity
`rArr x_(1).x_(2).x_(3) ....x_(n) = 1`..(i)
Using `AM ge GM, (x_(1) + x_(2) + ...+ x_(n))/(n) ge (x_(1).x_(2) ...x_(n))^(1//n)`
`rArr x_(1) + x_(2) + ...+ x_(n) ge n (1)^(1//n)` [from Eq. (i)]
Hence, sum of n positive numbers is never less than n.
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate: int(x^3)/((x-1)(x-2)(x-3))\ dx

Evaluate: int(x^(2)-3x)/((x-1)(x-2))dx

Evaluate: int(2x+1)/((x-2)(x-3))dx

Evaluate: int(x+3)/((x-1)(x^(2)+1))dx

11.Evaluate: int(dx)/((x-1)(x-2)(x-3))

Evaluate int(dx)/((x-1)(x-2)(x-3))

Evaluate int (x-1)/((x-2)(x-3)) dx

Evaluate :int(2x-3)/((x-1)^(2)(2x+3))dx

Evaluate int_(1)^3(x-1)(x-2)(x-3)dx

Evaluate: int(2x-3)/((x^2-1)(2x+3))dx