The value of ` ∫_-1^1 e^abs(x) dx` is: a) 2(e+1) , (b) 2(e-1) (c) 2(e-2) , (d) 3(e-1)

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d)

The value of int_0^1e^(x^2-x) dx is (a) 1 (c) > e^(-1/4) (d) < e^(-1/4)

The maximum value of (logx)/x is (a) 1 (b) 2/e (c) e (d) 1/e

The value of int_0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -1

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The value of int_1^e (1+x^2 In x)/(x+x^2 In x) dx is equal (a) In (1+e)e+In(1+e) (b) e-In(1+e)

The value of the integral int_-a^a (x e^(x^2))/(1+x^2)dx is (A) e^(a^2) (B) 0 (C) e^(-a^2) (D) a

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The value of int_(1//e )^(e )(|log x|)/(x^(2))dx , is

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0