Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Exponential functions - Integration - Applications.
Test Yourself 1 - Solutions.



The questions on this page focus on:
1. Finding original exponential functions.
2. Finding areas under exponential curves.
3. Finding areas between curves.
4. Finding volumes by rotating exponential curves.
5. Questions of the form Differentiate ... hence find.
6. applications to exponentials of the Reverse Chain Rule.

 
Finding original equations. 1. 2.
  3. 4.
Areas
(1 curve)		 5. Determine the area enclosed by the axes and y = 4ex - 1.

6.

  7. Calculate the exact area of the region bounded by the curve y = e2x, the
x-axis and the line x = 2.		 8. Calculate the exact area of the region bounded by the curve
y = e2x, the y axis and the line y = e2.
  9. Find the value of A given that the area of the region between y = ex and the x-axis between x = 0 and x = A is 2 units. 10. Find the area bounded by the curve

from x = -2 to x = 2.
Answer to 4 significant figures.

Answer.Area = 7.254 u2.
 

11. (i) Prove that the function is an even function.

(ii) Given that to three decimal places and that to three decimal places, determine the value of correct to 2 decimal places.
     
Areas
(2 curves)		 5. Find the area bounded by the curves
y = ex and y = e-x and the line x = 2.		 6. Find the area bounded by the curves
y = e½x and y = x and the lines

x = 0 and x = 2.
 

Find the exact area enclosed by the curves

y = e2x and y = e-x and the line x = 2.