# If `int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt `, then the value of f(1) is

Updated On: 26-7-2020

3.0 k+

100+

Answer

Text Solution

(1)/(2)

2

1

(3)/(4)

(1)/(2)

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FAQs on Application Of Integration

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

Property 2: If the limits of a definite integral are interchanged then its value changes.

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

Property 3:

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

Property 4: If

f(x)

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

int_0 ^a f(x) dx = int_0^a f(a-x) dx

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