If f(x)={{:(x^(2)" for "0lexle1),(sqrtx"...

If `f(x)={{:(x^(2)" for "0lexle1),(sqrtx" for "1lexle2):}" then "int_(0)^(2)f(x)dx=`

A

`(1//3)(4sqrt2+1)`

B

`(1//3)(4sqrt2-1)`

C

`(1//3)(2sqrt2-1)`

D

`(1//2)(3sqrt2-1)`

Text Solution

Verified by Experts

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

DEFINITE INTEGRATION
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1C|33 Videos
DEFINITE INTEGRATION
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1D|32 Videos
DEFINITE INTEGRATION
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1A|91 Videos
DE MOIVRE'S THEOREM
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-4|3 Videos
DIFFERENTIAL EQUATIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 2|15 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|{:(cosx,1,0),(1,2cosx,1),(0,1,2cosx):}|" then "int_(0)^(pi//2)f(x)dx=

int_(0)^(2)[|x|+|x-1|]dx=

Knowledge Check

If f(x)={{:(x^(2) " for " 0 le x le 1),(sqrt(x) " for "1 le x le 2):} then int_(0)^(2) f(x)dx=

A

`( 4 sqrt(2))/(3)`

B

`(4sqrt(2)-1)/(3)`

C

`(sqrt(2))/(3)`

D

`1/3`

If f(x)= {{:(x " for "x lt 1),(x-1 " for "x ge1):} then int_(0)^(2)x^(2)f(x)dx=

A

`5/3`

B

`3/5`

C

`- 5/3`

D

`- 3/5`

int_(0)^(2) [x^(2)-1]dx=

A

`4-sqrt(3)-sqrt(2)`

B

`4+sqrt(3)+sqrt(2)`

C

`sqrt(3)-1`

D

`sqrt(2)+1`

Similar Questions

Explore conceptually related problems

int_(0)^(1)(x)/(1+sqrtx)dx=

int_(0)^(1) (x^2)(1+x^2) dx =

int_(0)^(a) (f(x)+f(-x))dx=

If f(x)=|(cos x , 1, 0),(1, 2 cos x, 1),(0, 1, 2 cos x)| then int_(0)^(pi//2) f(x)dx=

Let f(x)={{:(e^(x)",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} , g(x)=int_(0)^(x)f(t)dt, x in[1,3] then g(x) has

DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1B

If f(x)={{:(x^(2)" for "0lexle1),(sqrtx" for "1lexle2):}" then "int(0)...
02:19
|
If int(-1)^(4)f(x)dx=4andint(2)^(4)[3-f(x)]dx=7" then "int(-1)^(2)f(x)...
03:05
|
If f(x) is an even function then int(-pi)^(pi)f(x)sinnxdx=
02:36
|
I=int(0)^(1)e^(x^(2))dx satisfies the inequality
03:01
|
int(-pi//2)^(pi//2)sinx.coshxdx=
01:47
|
int(-pi//2)^(pi//2)cosx.sinhxdx=
02:16
|
int(-pi//2)^(pi//2) sinx sechxdx=
02:34
|
int(-1)^(1)(coshx)/(1+e^(x))dx=
03:15
|
int(-1)^(1)(coshx)/(1+e^(2x))dx=
02:06
|
int(-pi//2)^(pi//2)(cosx)/(1-e^(x))dx=
03:32
|
Evaluate the definite integrals . underset(-pi//2)overset(pi//2)int ...
05:19
|
The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx,agt0 is
04:16
|
agt0,int(-pi)^(pi)(sin^(2)x)/(1+a^(x))dx=
03:50
|
int(-1)^(1)(ax^(3)+bx)dx=0 for
01:46
|
If int(0)^(x)f(t)dt=x+int(x)^(1)tf(t)dt, then the value of f(1) is
04:52
|
If f(y)=e^(y),g(y)=y:ygt0andF(t)=int(0)^(t)f(t-y)g(y)dy, then
03:28
|
The solution for x of the equation int(sqrt2)^(x)(dt)//t(sqrt(t^(2)-1)...
02:35
|
int(log2)^(t)(dx)/(sqrt(e^(x)-1))=(pi)/(6), then t=
04:09
|
int(0)^(pi//2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx=
02:18
|
int(0)^(pi//2)(cos^(3//2)x)/(cos^(3//2)x+sin^(3//2)x)dx=
02:40
|