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int0^(pi//2)1/(2+cos\ x)dx equals a. 1/3...

`int_0^(pi//2)1/(2+cos\ x)dx` equals a. `1/3tan^(-1)(1/(sqrt(3)))` b. `2/(sqrt(3))tan^(-1)(1/(sqrt(3)))` c. `sqrt(3)tan^(-1)(sqrt(3))` d. `2sqrt(3)tan^(-1)sqrt(3)`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. The value of int0^(2pi)sqrt(1+sin (x/2)dx is a. 0 b. 4 c. 2 d. 8

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  2. int0^(pi^2//4)(sinsqrt(x))/(sqrt(x))dx equals a. pi^2//8 b. pi//4 c. 2...

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  3. int0^(pi//2)1/(2+cos\ x)dx equals a. 1/3tan^(-1)(1/(sqrt(3))) b. 2/(sq...

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  4. 36/piint(pi//6)^(pi//3)(dx)/(1+sqrt(cotx)) equals to

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  5. Given that int0^oo(x^2)/((x^2+a^2)(x^2+b^2)(x^2+c^2))dx=pi/(2(a+b)(b+c...

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  6. int1^elogx\ dx= a. 1 b. e-1 c. e+1 d. 0

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  7. int1^(sqrt(3))1/(1+x^2)dx is equal to a. pi/(12) b. pi/4 c. pi/6 d. pi...

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  8. The value of int0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -...

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  9. If int0^a1/(1+4x^2)dx=\ pi/8 , then a equals a.pi/2 b. pi/4 c. 1/2 d. ...

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  10. int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0^1x^2f(x)dx=a^2,\ t h e n\ int...

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  11. The value of int(-pi)^pisin^3xcos^2x\ dx\ is a.(pi^4)/2 b. (pi^4)/4 c...

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  12. int(pi//6)^(pi//3)1/(sin2x)dx\ is equal to a. (log)e3 b. (log)"e"sqr...

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  13. int(-1)^1|1-x|dx is equal to a.-2 b. 2 c. 0 d. 4

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  14. int0^1x/((1-x)^(54))dx= a. 9(pi/2)^9 b. 10(pi/2)^9 c. (pi/2)^9 d....

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  15. (lim)(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} a. I n\ (1/3) b. I n\ (2/3)...

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  16. The value of the integral int(-2)^2|1-x^2|dx is a.4 b. 2 c. -2 d. 0

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  17. int0^(pi//2)1/(1+cot^3x)dx is equal to a 0 b. 1 c. pi//2 d. pi//4

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  18. int0^(pi//2)(sinx)/(sin x+cos x)dx equals to a. pi//2 b. pi//4 c. pi//...

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  19. int0^(pi//2)xsinx\ dx is equal to a. pi//2 b. pi//4 c. pi d. 1

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  20. int0^(pi//2)sin2xlogtanx\ dx\ is equal to a. pi//2 b. pi c. 0 d. 2pi

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