The value of `int_a^b(x-a)^3(b-x)^4dx` is

If m,n in N, then the value of int_a^b(x-a)^m(b-x)^n dx is equal to

The value of int_(a)^(b)(x-a)^(3)(b-x)^(4)dx is ((b-a)^(m))/(n). Then (m, n) is

Let f(x) is continuous and positive for x in [a , b],g(x) is continuous for x in [a , b]a n dint_a^b|g(x)|dx >|int_a^bg(x)dx| STATEMENT 1 : The value of int_a^bf(x)g(x)dx can be zero. STATEMENT 2 : Equation g(x)=0 has at least one root for x in (a , b)dot

int_a^bsqrt((x-a)(b-x)) dx , a > b

Evaluate: int_a^b x^3dx

Let a and b be two positive real numbers. Then the value of int_(a)^(b)(e^(x//a)-e^(b//x))/(x)dx is

The value of int_-3^3(a x^5+b x^3+c x+k)dx , where a, b, c and k are constants, depends only on

The value of integral int_(a)^(b)(|x|)/(x)dx , a lt b is :

Suppose f is continuous on [a,b] & f(a)=f(b)=0 & int_(a)^(b)f^(2)(x)dx=1 then the minimum value of int_(a)^(0)(f^(')(x))^(2)dx int_(a)^(b) x^(2)f^(2)(x)dx is k , then 8k is

The value of int_(-pi)^pisin^3xcos^2x\ dx\ is a. (pi^4)/2 b. (pi^4)/4 c. 0 d. none of these