The equation of the curve is y=f(x)dot ...

The equation of the curve is `y=f(x)dot` The tangents at `[1,f(1),[2,f(2)],a n d[3,f(3)]` make angles `pi/6,pi/3,a n dpi/4,` respectively, with the positive direction of x-axis. Then the value of `int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx` is equal to (a)`-1/(sqrt(3))` (b) `1/(sqrt(3))` (c)` 0` (d) none of these

Text Solution

AI Generated Solution

Topper's Solved these Questions

INEQUALITIES INVOLVING MEANS
CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
INTRODUCTION TO VECTORS
CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^('')dx+int_1^3f^('')dx is equal to -1/(sqrt(3)) (b) 1/(sqrt(3)) (e) 0 (d) none of these

If f(0)=0, f(3)=3 and f'(3)=4 , then the value of int_(0)^(1)xf'' (3x)dx is equal to

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

If f(x)=sqrt(x^2+6x+9) , then f^(prime)(x) is equal to (a) 1 for x<-3 (b) -1 for x<-3 (c) 1 for all x in RR (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (a) (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

If |f(x)-f(y)|le2|x-y|^((3)/(2)) AAx,yinR and f(0)=1 then value of int_(0)^(1)f^2(x)dx is equal to (a) 1 (b) 2 (c) sqrt2 (d) 4

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_e 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these

Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by (a)sqrt(x+3) (b) sqrt(x)+3 (c) x+sqrt(3) (d) none of these

CENGAGE ENGLISH-INTEGRALS-All Questions

int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logx dx is equal to (a) -pi/2logpi (...
Text Solution
|
If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf''(x)...
Text Solution
|
The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2...
Text Solution
|
The value of int1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b)...
Text Solution
|
If f(pi) = 2 int0^pi (f(x)+f^(x)) sinx dx=5, then f(0) is equal to (it...
Text Solution
|
If int1^2e^(x^2)dx=a ,t h e ninte^(e^4)sqrt(1n x)dx is equal to (a)...
Text Solution
|
int(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e...
Text Solution
|
The value of the expression (int0^a x^4(sqrt(a^2-x^2)))/(int0^a x^2(sq...
Text Solution
|
IfA=int0^pi(cosx)/((x+2)^2)dx ,t h e nint0^(pi/2)(sin2x)/(x+1)dx is eq...
Text Solution
|
int0^4((y^2-4y+5)sin(y-2)dy)/([2y^2-8y+11]) is equal to (a) 0 (b) 2 ...
Text Solution
|
The values of a for which the integral int0^2|x-a|dxgeq1 is satisfie...
Text Solution
|
evaluate: I=int(2x)/((x^2+1)(x^2+3))dx is
Text Solution
|
Let I=int1^3sqrt(3+x^3)dx , then the value of I will lie in the inte...
Text Solution
|
Ifinta^b|sinx|dx=8a n dint0^(a+b)|cosx|dx=9,t h e n (a) a+b=(9pi)/2 ...
Text Solution
|
If f(x)={0 ,where x=n/(n+1),n=1,2,3.... and 1 else where then the va...
Text Solution
|
The function f and g are positive and continuous. If f is increasing a...
Text Solution
|
A Function f(x) satisfies the relation f(x)=e^x+int0^1e^xf(t)dtdot T...
Text Solution
|
Let f(x) be positive, continuous, and differentiable on the interval ...
Text Solution
|
Letf: (0,oo)->R andF(x^3)=int0^ 3f(t)dt, if F(x^3)=x^3(x^2+x+1).Then f...
Text Solution
|
Ifg(x)=int0^x2|t|dt,then (a)g(x)=x|x| (b)g(x) is monotonic (c) g(x...
Text Solution
|