If a, b and c are real numbers, then the...

If a, b and c are real numbers, then the value of `underset(trarr0)(lim)((1)/(t)int_(0)^(t)(1+asinbx)^(c//x)dx)` equals

A

abc

B

`(ab)/(c )`

C

`(bc)/(a)`

D

`(ca)/(b)`

Text Solution

Verified by Experts

The correct Answer is:

A

Topper's Solved these Questions

INTEGRAL CALCULUS - 2
VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
INTEGRAL CALCULUS - 2
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
INTEGRAL CALCULUS - 2
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
FUNCTIONS
VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
INTEGRAL CALCULUS-1
VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If a, b and c are real numbers, then the value of lim_(trarr0) ((1)/(t)int_(0)^(t)(1+asinbx)^(c//x)dx) equals

For any real number x, the value of int_(0)^(x) [x]dx , is

The value of lim_(xto0)(1)/(x) int_(0)^(x)(1+ sin 2t)^(1/t) dt equals :

underset(xto0)("lim")(int_(0)^(x)t tan (5t)dt)/x^3 is equal to :

The value of lim_(xrarr0)(1)/(x^(3)) int_(0)^(x)(tln(1+t))/(t^(4)+4) dt

lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx equals

The value of lim_(a rarr oo)(1)/(a^(2))int_(0)^(a)ln(1+e^(x))dx equals

The value of lim_(xrarr0) (int_(0)^(x^2)sec^2t dt)/(x sin x) dx , is

Find the value of ln(int_(0)^(1) e^(t^(2)+t)(2t^(2)+t+1)dt)

The value of (int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt) is

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) ...
Text Solution
|
The value of lim(x to oo)(d)/(dx)int(sqrt(3))^(sqrt(x))(r^(3))/((r+1)...
Text Solution
|
If a, b and c are real numbers, then the value of underset(trarr0)(lim...
Text Solution
|
Let y = f(x) be a differentiable curve satisfying int(2)^(x)f(t)dt=(x...
Text Solution
|
If F(x)=(1)/(x^(2))overset(x)underset(4)int [4t^(2)-2F'(t)]dt then F'(...
Text Solution
|
Given f(x) where ={(x|x|,"for" xle -1),([x+1]+[1-x],"for"-1lt x lt...
Text Solution
|
If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx ...
Text Solution
|
The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...
Text Solution
|
Evaluate int-1^1 [x[1+sinpix]+1]dx, [.] is the greatest integer funct...
Text Solution
|
Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...
Text Solution
|
Let overset(a)underset(0)int f(x)dx=lambda and overset(a)underset(0)in...
Text Solution
|
The value of the integral overset(pi)underset(0)int (sin k x)/(sin x)...
Text Solution
|
The value of the integral int0^pi(x^2sinx)/((2x-pi)(1+cos^2x))\ dx
Text Solution
|
Let f : R->R be given by f(x) = {|x-[x]|, when [x] is odd and |x-[x...
Text Solution
|
If f(x) = sin x+cos x and g(x) = {:{((|x|)/(x),","x ne0),(2,","x=0):} ...
Text Solution
|
Let f(x)={(1-|x|","|x|le1),(0","|x|gt1):} and g(x)=f(x-1)"for all" x i...
Text Solution
|
Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...
Text Solution
|
Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...
Text Solution
|
Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...
Text Solution
|
Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...
Text Solution
|