PART I

a. The value of ¹_- e^2x dx is?

b. The r.m.s. value of f(t) = t² across [1,4] is ?

c. Determine the number c that satisfies the Mean Value Theorem for Integral of the function f(x) = 4x + 2 on the interval [1,4].

d. The degree of the equation [1+ (dy/dx)² ]³ = (d²y/dx²)² is?

e.Check whether the following statement is true or false.

d²y/dx² + y² =0is non- linear equation.

f.Find the differential equation of the family of curves y= Ae^x +Be^-x

,where A and B are arbitrary constants.

g. The general solution of R(z) = sin(2z)e^1-cos(2z) on [- , ] is?

h. Solve (x³ + y³)dy + x²y dx = 0

PART II: Read each question carefully and WRITE the answer that best fits the question.

a .Solve (1+x²)dy/dx + y = tan^-1x

b. Obtain the general equation of the curve whose slope at any point is equal to y - 2x.