Let f(x)=int ( z )^(2) (dy)/(sqrt(1+ y ^...

Let `f(x)=int _( z )^(2) (dy)/(sqrt(1+ y ^(3))).` The value of the integral `int _(0)^(2) xf (x ) dx` is equal to:

A

1

B

`1/3`

C

`4/3`

D

`2/3`

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

INDEFINITE AND DEFINITE INTEGRATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|16 Videos
INDEFINITE AND DEFINITE INTEGRATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|14 Videos
HYPERBOLA
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos
INVERSE TRIGONOMETRIC FUNTIONS
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|5 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=int _( x )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integral int _(0)^(2) xf (x ) dx is equal to:

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

The value of the integral int_-2^2(dx)/(x+1)^3 is

The value of definite integral int _(0)^(oo) (dx )/((1+ x^(9)) (1+ x^(2))) equal to:

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

The value of the definite integral int_0^(pi/2) ((1+sin3x)/(1+2sinx)) dx equals to

The value of the integral int_(0)^(a) (1)/(x+sqrt(a^(2)-x^(2)))dx , is

If f(x)=cos(tan^(-1)x) , then the value of the integral int_(0)^(1)xf''(x)dx is

The value of the definite integral int_(0)^(pi//3) ln (1+ sqrt3tan x )dx equals

VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let f(x)=int ( z )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integr...
Text Solution
|
int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...
Text Solution
|
If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...
Text Solution
|
Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x) be its inverse. ...
Text Solution
|
If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...
Text Solution
|
If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(s...
Text Solution
|
The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...
Text Solution
|
Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...
Text Solution
|
Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2)+1))")")dx...
Text Solution
|
If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...
Text Solution
|
Find the value of |a| for which the area of triangle included between ...
Text Solution
|
Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...
Text Solution
|
If I = int (0) ^(100) (sqrtx)dx, then the value of (9I)/(155) is:
Text Solution
|
Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...
Text Solution
|
If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...
Text Solution
|
Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...
Text Solution
|
underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...
Text Solution
|
The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...
Text Solution
|
Given a function g, continous everywhere such that g (1)=5 and int (0)...
Text Solution
|
If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...
Text Solution
|
Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...
Text Solution
|