Appln of Integration

Which of the following is a possible equation of the curve whose gradient at any point is given by $4e^{2x}+2$ ?

•  $8e^{2x}+C$  
  

•  $8e^{2x}+2x+C$  
  

•  $2e^{2x}+2x+C$  
  

•  $8e^{2x}+C$  
  

Given that the gradient of the curve at any point is given by $3\left(x^2+1\right)$ and the curve passes through  $\left(0,\ 2\right)$  and  $\left(1,\ p\right)$  , find the value of p. 

• 6

• 4

• 2

• 0

Find the area of the shaded region.

• 0.417

• 1.30

• 0.108

• 11.33

Which of the following represents the shaded area. (You may select more than 1 answer)

• $\int_0^1\ \ x-\sqrt{x}\ dx$

• $\int_0^1\ \sqrt{x}-x\ \ dx$
  

• $\int_0^1\ y\ -y^2\ dy$
  

• $\int_0^1\ \ y^2-y\ \ dy$
  

• $\int_0^1\sqrt{x}\ dx-0.5$

Which of the following represents the area bounded by the two curves  $y=e^{2x}$  and  $y=e^{\left(x-3\right)}$  from x=0 to x=1.

• 
• 
• 
• 

The area under the curve $y=3-ax^2$  from  $x=0$  to  $x=2$  is 4 sq units, find a.

• 0.25

• 0.5

• 0.75

• 1