# If `f(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2),` then

Updated On: 5-5-2021

5.6 k+

200+

Answer

Text Solution

f(x)=sqrt2x

f(x)=sqrt(2log _(e) x)

f(x)= sqrt(3x-1)

None of these

A

Transcript

Time | Transcript |
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00:00 - 00:59 | lacosta nearest if function of map of fact because through integration of 0 to add function of map of inverse DFT and 021 integration of cot inverse is equals to root 2 then which when you will be possible here are the dumb example to hear that causes in a function is given that half of b is equal to a f t invert the year in the following we will have we will put the limit over 02135 function of a property that will be equal to 2 am mentioned in the question and we can stay function of AP of the will be caused by a group to buy it ok so from this particular function we have the value integration that is 1021 |

01:00 - 01:59 | 1 by root 2021 1 by root 2 DT per Roti that is equal to 1 by root 2 the power 1 by 2 upon 1 by 2021 it will be equal to 1 by root 2 knowledge in here we will put the upper limit limit of it will come to X solving it we will have we can write route to as it will become root 2 root 2 is the function of ear effect will be equal to root 2 of of train number is the correct answer for the cost |

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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

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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