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If a be a positive integer, the number o...

If a be a positive integer, the number of values of a satisfying `int_(0)^(pi//2) {a^(2)((cos3x)/(4)+(3)/(4)cosx)+a sin x-20 cos x} dx le -(a^(2))/(2)`, is

A

only one

B

two

C

three

D

four

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Verified by Experts

The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. int(3pi//2)^(5pi//3) [2cos x]dx=

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  2. int(0)^(50pi)os x|dx=

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  3. If a be a positive integer, the number of values of a satisfying int(0...

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  4. The values of 'a' for which int0^(a) (3x^(2)+4x-5)dx lt a^(3)-2 are

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  5. If (-1,2) and and (2,4) are two points on the curve y=f(x) and if g(x)...

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  6. If I(1)=int(1-x)^(k) x sin{x(1-x)}dx and I(2)=int(1-x)^(k) sin{x(1-x)}...

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  7. If int(-pi//3)^(pi//3) ((a)/(3)|tan x|+(b tan x)/(1+sec x)+c)dx=0 wher...

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  8. If x=int(2)^(sint) sin^(-1) theta theta and y=int(n)^(sqrt(t))(sinthe...

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  9. |int(10)^(19) (sin x)/(1+x^(8))dx| is less than

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  10. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

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  11. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

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  12. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

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  13. int(0)^(pi) (1)/(1+3^(cosx)) dx is equal to

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  14. Let int(0)^(a) f(x)dx=lambda and int(0)^(a) f(2a-x)dx=mu. Then, int(...

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  15. The value of int(pi//4)^(3pi//4) (x)/(1+sin x) dx is equal to

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  16. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

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  17. The value of int(-1)^(1) max[2-x,2,1+x] dx is

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  18. int(0)^(pi//4) sin(x-[x]) dx is equalto

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  19. The value of the integral int(-1)^(1) (x-[2x])dx,is

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  20. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

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