Indefinite Integrals: JEE Questions & Solutions

If 0^1 4 ^-1(1 - 2x + 4x^2) dx = a ^-1(2) - b (5), where a, b N, then (2a + b) is equal to.

Let f(x) = (2 - x^2) e^x( 1 + x)(1 - x)^3/2 dx. If f(0) = 0, then f ( 12) is equal to:

Let I(x) = 3dx(4x+6) 4x^2+8x+3 and I(0) = 34 + 20. If I ( 12) = a 2b + c, where a, b, c N, (a, b) = 1, then a+b+c is equal to

Let f(t)= ( 1- ( e t)1- ( e t))dt, t1. If f(e^ /2)=-e^ /2 and f(e^ /4)= e^ /4, then equals

If f(x) satisfies the relation f(x)=e^x+ 0^1 (y+x e^x)f(y) dy, then e+f(0) is equal to

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)= dx2 ( 32)^x+2x ( 12)^x 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 ( x ^-1 x + ^-1 x (1 - x^2)^3/2 + x1 - x^2) dx = g(x) + C, where C is the constant of integration, then g ( 12) equals:

If 2x^2 + 5x + 9 x^2 + x + 1 dx = x^2 + x + 1 + x^2 + x + 1 + e ( | x + 12 + x^2 + x + 1 |) + C, where C is the constant of integration,…

Let f be a real-valued continuous function defined on the positive real axis such that g(x) = 0^x t f(t) dt. If g(x^3) = x^6 + x^7, then…

If f(x) = 1x^1/4 (1 + x^1/4) dx, f(0) = -6, then f(1) is equal to:

If 24 ( 0^ 4 [ ( 4x - 12) + [2 x] ] dx) = 2n +, where [.] denotes the greatest integer function, then is equal to:

If ( 1 + x^2 + x)^10 ( 1 + x^2 - x)^9 dx = 1m ( ( 1 + x^2 + x)^n ( n 1 + x^2 - x)) + C, where m, n N and C is the constant of integration,…

The integral x^8 - x^2(x^12 + 3x^6 + 1) (x^3 + 1x^3) dx is equal to:

If ^3/2x + ^3/2x ^3 x ^3 x (x-) dx = A x - B x + C, where C is the integration constant, then AB is equal to:

Let f(x) = -x^x (|t| - t^2)e^-t^2 dt and g(x) = 0^x^2 t^1/2e^-t dt. The value of f( 9) + g( 9) is:

The integral 3/4^1/4 (2 ^-1 ( 1-x1+x)) dx is equal to:

The minimum value of the function f(x) = 0^2 e^|k-t| dt is:

Let f(x) = 2xx^2 + 1(x^2 + 3) dx. If f(3) = 12( e 5 - e 6), then f(4) is equal to:

If 2x - 1 dx = e ( 2x +) + 2x ( 1 + 2x) ( 1) + constant, then - is equal to

Let (0, 1) and = (1 -). Let Pn(x) = x + x^22 + x^33 + + x^nn, x (0, 1). Then the integral 0^ 11 - t dt is equal to:

Let 0. If ^x x x + - x dx = 16 + 20 215, then is equal to:

If I(x) = e^ ^2x x( 2x - x) dx and I(0) = 1, then I ( 3) is equal to:

For,,, N, if ( xe)^2x + ( ex)^2x x dx = 1 ( xe)^ x - 1 ( ex)^ x + C where e = n=0^ 1n! and C is the constant of integration, then + 2 + 3 -…

The value of the integral 2^- 2 e^x ( ( e^x + 1 + e^2x)) dx is equal to:

Let I(x) = x+7x dx and I(9) = 12 + 7 e 7. If I(1) = + 7 e (1+2 2), then ^4 is equal to:

Let for x R, S0(x) = x, Sk(x) = Ck x + k 0^x Sk-1(t) dt where C0 = 1, Ck = 1 - 0^1 Sk-1(x) dx, k = 1, 2, 3,. Then S2(3) + 6C3 is equal to: