Home
Class 12
MATHS
Let n be a positive integer such that In...

Let `n` be a positive integer such that `I_n=intx^nsqrt(a^2-x^2)dx`Now answer the following question: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

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

intx^3/(1+x^2)^2dx

intx/(x^2+2)^(1/3)dx

int(x^3dx)/(sqrt(1+x^2)) is equal to (A) 1/3sqrt(1+x^2)(2+x^2)+C (B) 1/3sqrt(1+x^2)(x^2-1)+C (C) 1/3(1+x^2)^(3/2)+C (D) 1/3sqrt(1+x^2)(x^2-2)+C

Differentiate the following functions with respect to x (i) (2x+3)/(x^2-5) (ii) (x+3)/(x^2+1)

The anti derivative of (sqrt(x)+1/(sqrt(x))) equals(A) 1/3x^(1/3)+2x^(1/2)+C (B) 2/3x^(2/3)+1/2x^2+C (C) 2/3x^(3/2)+2x^(1/2)+C (D) 3/2x^(3/2)+1/2x^(1/2)+C

The value of (lim)_(x->(3pi)/4)(1+t a n x1/3)/(1-2cos^2x) is (a) -1//2 (b.) -2//3 (c). -3//2 (d). -1//3

Choose the correct answer intsqrt(1+x^2)dx is equal to(A) x/2sqrt(1+x^2)+1/2log|(x+sqrt(x+x^2))|+C (B) 2/3(1+x^2)^(3/2)+C (C) 2/3x(1+x^2)^(3/2)+C (D) (x^2)/2sqrt(1+x^2)+1/2x^2log|x+sqrt(1+x^2)|+C

If I_n=int x^nsqrt(a^2-x^2)dx, prove that I_n=-(x^(n-1)(a^2-x^2)^(3/2))/((n+2))+((n+1))/((n+2))a^2I_(n-2)

Choose the correct answer intx^2e^(x^3)dx equals(A) 1/3e^(x^3) +C (B) 1/3e^(x^2)+C (C) 1/2e^(x^3)+C (D) 1/2e^(x^2)+C

The value of lim_(xto oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+....nx^(1//n))/((2x-3)^(1//2)+(2x-3)^(1//3)+....+(2x-3)^(1//n)) is