Home
Class 12
MATHS
If the integral int(0)^(10) ([sin2pi x])...

If the integral `int_(0)^(10) ([sin2pi x])/(e^(x-[x]))dx=alpha e^(-1)+beta e^(-(1)/(2))+gamma`, where `alpha, beta, gamma` are integers and [x] denotes the greatest integer less than or equal to x, then the value of `alpha+beta+gamma` is equal to :

A

0

B

25

C

20

D

10

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If the value of the integral int_0^5 (x + [x])/(e^(x - [x])) dx = alphae^(-1) + beta ,where alpha, beta in R, 5alpha + 6beta = 0, and [x] denotes the greatest integer less than or equal to x, then the value of (alpha + beta )^2 is equal to :

int_0^10([sin2pix])/e^(-[x]+x)dx=alphae^(-1)+betae^(-1/2)+gamma . then find alpha+beta+gamma

If alpha, beta , gamma are the zeros of the polynomial x^(3)-6x^(2)-x+30 then the value of (alpha beta+beta gamma+gamma alpha) is

If alpha + beta + gamma=pi, then the value of sin ^(2) alpha + sin ^(2) beta - sin^(2) gamma is equal to

Let alpha,beta,gamma be the complex roots of x^(3)-1=0 then,alpha+beta+gamma is equal to

If alpha beta gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If alpha and beta are the solution of sinx=-(1)/(2) in [0, 2pi] and alpha and gamma are the solutions of cos x=-(sqrt3)/(2) in [0, 2pi] , then the value of (alpha+beta)/(|beta-gamma|) is equal to

If int_(pi/6)^(pi/3) sqrt (1- sin 2x) dx = alpha beta sqrt 2 gamma sqrt 3 , where alpha, beta and gamma are rational numbers, then 3 alpha 4 beta-gamma is equal to _______.

If the roots of x(3-x^2)+2x^2=0 are alpha,beta,gamma then the value of alpha+beta+gamma+1 is ________ .