Week 7 Integration

Question 1

Integration of X^n dx =

Answer 1

(1/n+1)X(n+1)

Question 2

Integration of 1/X dx =

Answer 2

Log(x) + c

Question 3

Integration of e^x =

Answer 3

E^x + c

Question 4

Integration of sim(x) dx =

Answer 4

-cos(x) + c

Question 5

Integration of cos(x) dx

Answer 5

Sin(x) + c

Question 6

What is integration by substitution

Answer 6

Perform a substitution to get an integrated I a form that we can do.

Question 7

What is the substitution of
Sqrt( a^2 - x^2)

Answer 7

You sub x = asin(u)

Question 8

What is the substitution of
Sqrt(x^2 + a^2)

Answer 8

Sub x = atan(u).
Or
You can sub sinh(u)

Question 9

What does cosh(x)

Answer 9

= 1/2* (e^x + e^-x)

Question 10

Sinh(x) =

Answer 10

1/2 * (e^x - e^-x)

Question 11

D/dx cosh(x)

Answer 11

= sinh(x)

Question 12

D/dx sinh(x)

Answer 12

=Cosh(x)

Question 13

Cosh^2(x) - sinh^2(x)

Answer 13

= 1

Question 14

Integration using hyperbolic functions
Sqrt(x^2+a^2)

Answer 14

Sub x = asinh(u)

Question 15

F the integrated looks like

Sqrt(x^2 - a^2)

Answer 15

Sub x = acosh(u)