ADVANCED HIGH SCHOOL MATHEMATICS INTEGRATION EXERCISES

ADVANCED HIGH SCHOOL MATHEMATICS

INTEGRATION EXERCISES

Ian Cooper email: matlabvisualphysics@

To find a Question or Answer use the find function: control f Question 4 Q4 Answer 15 A15

QUESTIONS

Evaluate the following integrals

Q1

I

1

x

x

2

dx

Q2

x2

I

x2

1

dx

Q3

I

x

1 x2

4

dx

1

Q4

I

x 1

x

dx

Q5

I /4sin2 (2x) dx 0

Q6

I sin2(x)cos(x) dx

Q7

I sin2(x)cos3(x) dx

Q8

dx

I a2 x2

Q9

sin1 x dx

Q10

I

1

x

x

2

dx

Q11

x2

I

x2

1

dx

Q12

I

x

1 x2

4

dx

Q13

I

x 1

x

dx

Q14

I /4sin2 (2x) dx 0

Q15

I sin2(x)cos(x) dx

2

Q16

I sin2(x)cos3(x) dx

Q17

dx

I

a2 x2

Q18

I sin1 x dx

Q19

I e3 cos(4 ) d

Q20

I xn loge (x) dx

Q21

I xn ex dx and evaluate the integral when n = 3

Q22

I cosn x dx and evaluate the integral when n = 4

Q23

I

x2

dx 4x

1

Q24

dx

I 3 x2 6 x 10

Q25

3x 2

I

x2

dx 4x 1

3

Q26

3 1 x

dx

1 x2 1 x2

Q26

1

ex

1/ 2

1 dx

0

Q28

dx

I x2 1 x

9x2

Q29

I 2x2 7x 3 dx

3x2 2 x 1

Q30

I x2 1 x2 2 dx

Q31

I

2 x2 3x 1 x3 x2 x 1 dx

4

ANSWERS

A1

I

1

x

x

2

dx

I

1

x

x

2

dx

I

1

2 x

1 x2

dx

1 I x 2 loge (x) x K

A2

x2

I

x2

1

dx

x2

B Ax2 A B

N

A

x2 1

x2 1

x2 1

A 1 B 1

I

1

x

1 2

1

dx

dx a2 x2

1 a

tan

1

x a

I x tan1(x) K

5

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