ZCA 110 Calculus Test 3.                                           Venue: DPD; Date: Friday, 11 am- 12pm 9 Dec 2016
Name:                                                                                                                                               Matrix No:
Q1.Given that u(x) is a differentiable function, explain how the following integration rule is derived. [Hint: You may have to start from the differentiation of (u^(
n))]
 ∫(u^(
n))du=(1/(n+1))(u^(
n+1))+C; n≠-1.
 
  
 
 
 


Q2.Given  f(x)=((sin x+xcos x)/(Exp(x)+Exp(-x))), evaluate(∫_(-π)^π)f(x)dx. 


 

Q3. Find the length of the curve parametrised by x=2(t^2)+1 , y=2(t^3),  0 ≤ t ≤ 1.








Q4. Explain how the following differential result is derived: (d/dx)(e^x)=(e^x).






Q5. Prove ((e^(Subscript[x, 2]))/(e^(Subscript[x, 1])))=(e^(Subscript[x, 2]))·(e^(-(Subscript[x, 1]))), for all real numbers (Subscript[x, 1]) and (Subscript[x, 2]).