Home
Class 12
MATHS
Let n be a positive interger such that I...

Let n be a positive interger such that `I_n=intx^nsqrt(a^2-x^2)dx`
Answer the following the question based on above passage:
The value of `I_1` is

A

`2/3(a^2-x^2)^(1//2)`

B

`1/3(a^2-x^2)^(3//2)`

C

`-2/3(a^2-x^2)^(3//2)`

D

`-1/3(a^2-x^2)^(3//2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    PATHFINDER|Exercise QUESTION BANK|39 Videos

  • MATRICES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). Answer the following the question based on above passage: Which of the following is true:?

Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). Answer the following the question based on above passage: f(x) is given by

Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(1) = 2 Answer the following question based on above passage : f(x) - f(y) is equal to

Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(1) = 2 Answer the following question based on above passage : f'(3) is equal to

Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(1) = 2 Answer the following question based on above passage : f€ is equal to

Let x in R be any real number such that xlies between any two consecutive integers say n-1 and n, i.e., n-1 ltxlen then we can always find this unique integer n. Let us call this n as super integral value of x. We denote it symbolically as (x) For example: if x=2.63,then (x)=3,if x=-2.63,then (x)=-2 Answer the following questions are based on above passage:The range of the function y= y=((x))/x if x in (-infty,0) ,is

Let f_1(x,y)-=ax^2+2hxy+by^2=0 and let f_(i+1)=0 denotes the equation of the bisectors of f_i(x,y)=0 for all i=1,2,3…. Answer the following question based on above passage: Equation f_2(x,y)=0 is

Let f_1(x,y)-=ax^2+2hxy+by^2=0 and let f_(i+1)=0 denotes the equation of the bisectors of f_i(x,y)=0 for all i=1,2,3…. Answer the following question based on above passage: Equation f_3(x,y)=0 is

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

Newton-Leinbnitz's formula states that d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)} Answer the following questions based on above passage: Let f(x) be a differentiable function and f(1)=2, If lim_(xrarr1)int_2^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is equal to

PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

    Text Solution

    |

  2. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

    Text Solution

    |

  3. Let n be a positive interger such that In=intx^nsqrt(a^2-x^2)dx Answer...

    Text Solution

    |

  4. Let n be a positive interger such that In=intx^nsqrt(a^2-x^2)dx Answer...

    Text Solution

    |

  5. Match List-I with List-II

    Text Solution

    |

  6. Match List - I with List-II Let the functions defined in List - I ha...

    Text Solution

    |

  7. If int (sqrttanx + sqrtcotx) dx = a tan^-1 ((tan x - 1)/sqrt(b tan x))...

    Text Solution

    |

  8. If int((cos8x-cos7x)/(1+2cos5x))dx=(sin3x)/a-(sin2x)/b+c then the last...

    Text Solution

    |

  9. If int(1+cos8x)/(tan2x- cot2x)dx= acos8x +c, then find the value of a.

    Text Solution

    |

  10. If int(x+(cos^-1 3x)^2)/sqrt(1-9x^2)dx=Asqrt(1-9x^2)+B(cos^-1 3x)^3+C,...

    Text Solution

    |

  11. If int(sinx^8-cosx^8)/(1-2sinx^2cosx^2)dx= asin2x +c, then find the va...

    Text Solution

    |

  12. Evaluate int(dx)/((2x-x^2)^(3//2))

    Text Solution

    |

  13. Evaluateintsqrt(cos2x)/sinx dx

    Text Solution

    |

  14. Evaluateint(dx)/(cosx+cosecx)

    Text Solution

    |

  15. Evaluateintsqrt(secx-1)dx, 0ltxltpi/2

    Text Solution

    |

  16. Evaluateint(dx)/(x^2(x^4+1)^(3//4)), xgt0

    Text Solution

    |

  17. Evaluateintcos2theta log((costheta+sintheta)/(costheta-sintheta))d the...

    Text Solution

    |

  18. Evaluateintcos(2cot^-1sqrt((1-x)/(1+x)))dx, -1ltxle1

    Text Solution

    |

  19. Evaluateint(2xdx)/(1+x^4)

    Text Solution

    |

  20. Find the value of int(sinx+cosx)/(sin(x-alpha)) dx=

    Text Solution

    |