1. In each case write down the most general anti?derivative associated with the given function. (a) f(x)=x^2 - 3cos(2x)+1 x Element R, (b) g(x)=(13x - 1)^7+ root x-1 x less than or equal to 1, (c) h(x) = (x + 1)sin(x^2+2x) ? 1/x^2. X not equal to 0.2. Calculate the area of the finite region bounded by tile parabolas given by y = (x + 1)(x - 1), and y = -(1 + 4x + x^2) 3. For what value of k is the area under the graph of y = 3x^2 + 4kx between x = 0 and x = 1, equal to 3? 4. Evaluate (a) Integrate limit between 0 to 1 x(x^3+2x +1)dx, (b) Integrate limit between 0 to Pi x + cos(x) sin^2(x) dx.
