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

Exponential functions - Integration - basic.
Test Yourself 1.


 

The types of questions on this page which can be reached using the relevant hyperlinks are:

1. Finding indefinite and definite integrals.

2. Finding the equations of curves.

 

Integrate the following indefinite integrals:

1. 2. 3.
4. 5. 6.
7. 8. 9. Find y if .
10. 11.

12. Find the primitive of
13. 14. 15.
 

Evaluate the following definite integrals leaving your answer in the exact form for Q16-21 and to two decimal places for Q 22-27:

16. 17. 18.
19.

 

 20. 21.
22.
Answer.e4/2 + e2 +2.5 = 22.41.		 23. Given that

evaluate .

Answer.8.66.		 24. Answer.23.55.
25.
Answer.1.875.		 26.
Answer.1/12.		 27.
28. 29. 30.
 

Finding equations of curves:

31. The gradient of a curve is given by

y' = e2-x

The curve passes through the point (0, 1).

What is the equation of the curve?

Answer.y = e2 +1 - e2-x.		 32. Given and when x = 1, y = 3,

find y as a function of x.

Answer.y = -e1-x + 4.
33. If , find the value of m (to one significant figure).
Answer.m = 2.		 34. If and when x = 0,
y = 2 and , find the value of y
when x = 1.
Answer.y = 7.82.
35. If

and , find the equation for y in terms of x.

 36.