Indefinite Integration questions
503 published questions with worked solutions.
- If x^2+x+1 x^2+2x+1 =A+ B x+1 + C (x+1)^2 , then A-B is equal to
- If x^3 (2x-1)(x+2)(x-3) =A+ B 2x-1 + C x+2 + D x-3 , then A is equal to
- The partial fraction of 3x^3-8x^2+10 (x-1)^4 is
- If a real valued function f of a real variable x such that 1 (1+x) (1+x^2 ) = A 1+x + f(x) 1+x^2 , then f(x) is equal to
- Let a,b and c be such that 1 (1-x)(1-2x)(1-3x) = a 1-x + b 1-2x + c 1-3x , then a1+ b3+ c5 is equal to
- If x+1 (2x-1)(3x+1) = A 2x-1 + B 3x+1 , then 16A+9B is equal to
- If 3x+2 (x+1) (2x^2+3 ) = A x+1 + Bx+C 2x^2+3 , then A+C-B is equal to
- Let f(x) = ( 16x+24 x^2+2x-15 )dx. If f(4) = 14log_e(3) and f(7) = log_e(2^ 3^ )$, α, β ∈ ℕ, then α + β is equal to:
- The value of the integral _ /6 ^ /3 ( 4- ^2x ^4x )dx is:
- The value of the integral _ -1 ^2 _e (x + x^2+1 )dx is :
- Let 2 - x 3 + x dx = 12( x + _e| x + x|) + C, where C is the constant of integration. Then + is equal to
- The integral (x^8 - x^2)dx (x^ 12 + 3x^6 + 1) ^ -1 (x^3 + 1 x^3 ) is equal to:
- If _0^1 1 3+x + 1+x dx = a + b 2 + c 3, where a, b, c are rational numbers, then 2a + 3b – 4c is equal to
- If ^ 3/2 x + ^ 3/2 x ^3x ^3x (x- ) dx = A x - + B - x + C, where C is the integration constant, then AB is equal to
- If _ /6 ^ /3 1 - 2x ,dx = + 2 + 3, where α, β and γ are rational numbers, then 3α + 4β – γ is equal to ________.
- For x ∈ (−π/2, π/2), if y(x) = cosec ,x + x cosec ,x x + x ^2x dx, and _ x 2 y(x) = 0 then y ( 4 ) is equal to-
- If the integral 525 _0^ /2 2x ^ 11 2 x (1 + ^ 52 x )^ 12 dx is equal to (n√2 − 64), then n is equal to ________.
- For real numbers , , and , if (x^2-1)+ ^ -1 ( x^2+1 x ) (x^4+3x^2+1)+ ^ -1 ( x^2+1 x ) dx= _e ( ^ -1 ( x^2+1 x ) )+ ^ -1 (...
- The integral (2x-1 ) 2x-1^2+5 4x^2-4x+6 dx is equal to (where c is a constant of integration)
- If f(x)= 5x^8+7x^6 (x^2+1+2x^7)^2 dx, (x 0), f(0)=0 And f(1) = 1 K , then the value of K is
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