Indefinite Integration questions
503 published questions with worked solutions.
- At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number...
- If f(x)dx = (x), then x^5 f(x^3)dx is equal to -
- If ( x)^ -11/2 ( x)^ -5/2 dx = - p_1 q_1 ( x)^ 9/2 - p_2 q_2 ( x)^ 5/2 - p_3 q_3 ( x)^ 1/2 + p_4 q_4 ( x)^ -3/2 + C, where p_i...
- Let f(x) = (2-x^2) e^x ( 1+x )(1-x)^ 3/2 dx. If f(0) = 0, then f ( 1 2 ) is equal to :
- Let I(x) = 3dx (4x+6)( 4x^2+8x+3 ) and I(0) = 3 4 +20. If I ( 1 2 ) = a 2 b +c, where a, b, c N , gcd(a,b)=1, then a+b+c is equal...
- Let f(t) = ( 1- ( _e t) 1- ( _e t) )dt, t>1. If f(e^ /2 ) = -e^ /2 and f(e^ /4 ) = e^ /4 , then equals
- If ( 1-5 ^2 x ^5 x ^2 x )dx = f(x) + C where C is the constant of integration, then f ( 6 ) - f ( 4 ) is equal to
- Let f(x)= dx x^ (2/3) +2x^ (1/2) be such that f(0)=-26+24 _e(2). If f(1)=a+b _e(3), where a,b Z, then a+b is equal to:
- If e^x ( x ^ -1 x 1-x^2 + ^ -1 x (1-x^2)^ 3/2 + x 1-x^2 )dx = g(x)+C, Where C is the constant of integration, then g ( 1 2 )...
- Let x^3 x ,dx = g(x) + C, where C is the constant of integration. If 8 (g ( 2 ) + g' ( 2 ) ) = ^3 + ^2 + , , , Z. Then + - equals...
- Let I(x) = dx (x-11)^ 11/13 (x+15)^ 15/13 . If I(37) - I(24) = 1 4 ( 1 b^ 1/13 - 1 c^ 1/13 ), b, c N, then 3(b+c) is equal to-
- If 2x^2+5x+9 x^2+x+1 dx = x x^2+x+1 + x^2+x+1 + _e |x+ 1 2 + x^2+x+1 | + C, where C is the constant of integration, then + 2 is...
- If f(x) = 1 x^ 1/4 (1+x^ 1/4 ) dx, f(0) = –6, then f(1) is equal to:
- Let f : R → R be a twice differentiable function such that f(2) = 1. If F(x) = xf(x) for all x ∈ R, _0^2 xF'(x)dx = 6 and _0^2...
- 4 _0^1 ( 1 3+x^2 + 1+x^2 )dx - 3 _e( 3 ) is equal to :
- Let f(x) = x^3 3-x^2 ,dx. If 5f( 2) = -4, then f(1) is equal to
- If ( 1+x^2 +x)^ 10 ( 1+x^2 -x)^9 dx = 1 m (( 1+x^2 +x)^n(n 1+x^2 -x) )+c where C is the constant of integration and m, n N , then...
- The integral (1 + x - 1 x )e^ x + 1 x ,dx is equal to
- The integral 2x^ 12 + 5x^9 (x^5 + x^3 + 1)^3 dx is equal to - (where C is an arbitrary constant)
- Let I_n = ^nx ,dx, (n > 1). If I_4 + I_6 = a ^5x + bx^5 + C, where C is a constant of integration, then the ordered pair (a, b)...
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