`inta^(2x+3)dx`

Evaluate: inta^(x)e^(x)dx

STATEMENT 1: If f(x) is continuous on [a , b] , then there exists a point c in (a , b) such that int_a^bf(x)dx=f(c)(b-a) STATEMENT 2: For a

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

STATEMENT 1: int_0^pisin^(100)xcos^(99)xdx is z ero . STATEMENT 2: int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx ,a n d for odd function, int_(-a)^af(x)dx=0

If f(x) is monotonic differentiable function on [a , b] , then int_a^bf(x)dx+int_(f(a))^(f(b))f^(-1)(x)dx= (a) bf(a)-af(b) (b) bf(b)-af(a) (c) f(a)+f(b) (d) cannot be found

Evaluate: int_a^b x^3dx

If int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

Show that int_a^b(|x|)/x dx=|b|-|a|dot

Evaluate: int_a^b e^x dx using limit of sum

Evaluate: int_a^bsinx dx using limit of sum