# `int_(0)^(pi//3) [sqrt3 tan x] dx`, where [.] denotes the greatest integer function is

Updated On: 2-12-2021

2.0 k+

100+

Answer

Text Solution

(pi)/(2)- "tan"^(-2) (2)/(sqrt3)

(5pi)/(6) - "tan"^(-1) (2)/(sqrt3)

(5pi)/(6)

none

A

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FAQs on Definite Integral

Fundamental Theorem of Definite Integration

int_a ^b f(x) dx = phi(b) - phi(a)

Examples:

int_2 ^4 x / (x^2 + 1) dx

Definite integration by substitution

Examples:

int_0 ^1 sin^-1 ((2x )/ (1 + x^2)) dx

Property 1: Integration is independent of the change of variable.

int_a ^b f(x) dx = int_a ^b f(t) dt

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Property 3:

int_a ^b f(x) dx = int_a ^c f(x)dx + int_c ^b f(x) dx

Property 4: If

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is a continuous function on

[a,b]

then

int_a ^b f(x) dx = int_a ^b f(a+b-x) dx

Property 5: If

f(x)

is a continuous function defined on

[0,a]

then

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