Indefinite Integration questions
503 published questions with worked solutions.
- Let n ≥ 2 be a natural number and 0 < < 2. Then ( ^n - )^ 1/n ^ n+1 d is equal to: (where C is a constant of integration)
- Let (0, 2 ) be fixed. If the integral x + x - dx = A(x) 2 + B(x) 2 + C, where C is a constant of integration, then the functions...
- A value of α such that _ ^ +1 dx (x + )(x + + 1) = _e ( 98 ) is:
- If d ^2 ( 2 + 2 ) = +2 _e|f( )|+C where C is a constant of integration, then the ordered pair ( ,f( )) is equal to -
- The integral dx (x+4)^ 8/7 (x-3)^ 6/7 is equal to : (where C is a constant of integration)
- If f'(x)= ^ -1 ( x+ x), - 2 <x< 2 , and f(0) = 0, then f(1) is equal to
- If the value of the integral _0^ 1/2 x^2 (1-x^2)^ 3/2 dx is k 6 , then k is equal to -
- If ^ -1 ( x 1+x )dx=A(x) ^ -1 ( x )+B(x)+C, where C is a constant of integration, then the ordered pair (A(x), B(x)) can be -
- If ^5x ,dx = x x ( ^2x + 32 ) + _e | x2 | + C where α, β ∈ R and C is constant of integration, then the value of 8(α + β) equals...
- _0^ /4 ^2x ^2x ( ^3x + ^3x)^2 dx is equal to
- If x ,dx ^3x(1+ ^6x)^ 2/3 =f(x)(1+ ^6x)^ 1/ +c where c is a constant of integration, then f ( 3 ) is equal to -
- If 1 a^2 ^2x + b^2 ^2x dx = 1 12 ^ -1 (3 x) + constant, then the maximum value of a sin x + b cos x, is:
- Let I(x) = 6 ^2x(1 - x)^2 dx. If I(0) = 3, then I ( 12 ) is equal to:
- Let _ ^ _e4 dx e^x - 1 = 6. Then eᵅ and e⁻ᵅ are the roots of the equation:
- If 1 [5] (x - 1)^4(x + 3)^6 dx = A ( x - 1 x + 3 )^B + C, where C is the constant of integration, then the value of α + β + 20AB...
- The integral ( x x x+ x )^2dx is equal to (where C is a constant of integration) :
- Let f(x)= x (1+x)^2 dx (x ≥ 0). Then f(3) – f(1) is equal to :
- The integral _ /6 ^ /3 x ^23x(2 x 3x+3 x 6x)dx is equal to :
- If (e^ 2x +2e^x-e^ -x -1)e^ (e^x+e^ -x ) dx=g(x)e^ (e^x+e^ -x ) +c, where c is a constant of integration, then g(0) is equal to :
- If ,d 5+7 -2 ^2 =A _e|B( )|+C, where C is a constant of integration, then A can be :
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